Soft intersection almost ideals of semigroups

Yıl 2024, Cilt: 4 Sayı: 2, 466 – 481, 31.07.2024

Aslıhan Sezgin Aleyna İlgin

https://doi.org/10.61112/jiens.1464344

Öz

The aim of this study is to present the notion of soft intersection almost left (respectively, right) ideal of a semigroup which is a generalization of nonnull soft intersection left (respectively, right) ideal of a semigroup and investigate the related properties in detail. We show that every idempotent soft intersection almost (left/right) ideal is a soft intersection almost subsemigroup. Besides, we acquire remarkable relationships between almost left (respectively, right) ideals and soft intersection almost left (respectively, right) ideals of a semigroup as regards minimality, primeness, semiprimeness and strongly primeness.

Anahtar Kelimeler

soft set, semigroup, almost (left/right) ideal, soft interscetion almost (lefT/right) ideal

Proje Numarası

YOK

Kaynakça

  • Grosek O, Satko L (1980) A new notion in the theory of semigroup. Semigroup Forum 20: 233–240.
  • Bogdanovic S (1981) Semigroups in which some bi-ideal is a group. Univ u Novom Sadu Zb Rad Prirod Mat Fak Ser Mat 11:261–266.
  • Wattanatripop K, Chinram R, Changphas T (2018) Quasi-A-ideals and fuzzy A-ideals in semigroups. J Discrete Math Sci Cryptogr 21:1131–1138.
  • Kaopusek N, Kaewnoi T, Chinram R (2020) On almost interior ideals and weakly almost interior ideals of semigroups. J Discrete Math Sci Cryptogr 23:773–778.
  • Iampan A, Chinram R, Petchkaew P (2021) A note on almost subsemigroups of semigroups. Int J Math Comput Sci 16 (4):1623–1629.
  • Chinram R, Nakkhasen W (2022) Almost bi-quasi-interior ideals and fuzzy almost bi-quasi-interior ideals of semigroups. J Math Comput Sci 26:128–136.
  • Gaketem T (2021) Almost bi-interior ideal in semigroups and their fuzzifications. Eur J Pure Appl Math 15 (1):281-289.
  • Wattanatripop K, Chinram R, Changphas T (2018) Fuzzy almost bi-ideals in semigroups. Int J Math Comput Sci 13:51–58.
  • Krailoet W, Simuen A, Chinram R, Petchkaew P (2021) A note on fuzzy almost interior ideals in semigroups. Int J Math Comput Sci 16:803–808.
  • Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37(1):19-31.
  • Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(1):555-562.
  • Pei D, Miao D (2005) From soft sets to information systems. In: Proceedings of Granular Computing. IEEE 2:617-621.
  • Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547-1553.
  • Sezgin A, Atagün AO (2011) On operations of soft sets. Comput Math App l61(5):1457-1467.
  • Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56(10):2621-2628.
  • Ali MI, Shabir M, Naz M (2011) Algebraic structures of soft sets associated with new operations. Comput Math Appl 6:2647–2654.
  • Sezgin A, Shahzad A, Mehmood A (2019) New operation on soft sets: Extended difference of soft sets. J New Theory 27:33-42.
  • Stojanovic NS (2021) A new operation on soft sets: Extended symmetric difference of soft sets. Military Technical Courier 69(4):779-791.
  • Sezgin A, Atagün AO (2023) New soft set operation: Complementary soft binary piecewise plus operation. Matrix Science Mathematic 7(2):125-142.
  • Sezgin A, Aybek FN (2023) New soft set operation: Complementary soft binary piecewise gamma operation. Matrix Science Mathematic 7(1):27-45.
  • Sezgin A, Aybek FN, Atagün AO (2023) New soft set operation: Complementary soft binary piecewise intersection operation. BSJ Eng Sci 6(4):330-346.
  • Sezgin A, Aybek FN, Güngör NB (2023) New soft set operation: Complementary soft binary piecewise union operation. Acta Informatica Malaysia 7(1): 38-53.
  • Sezgin A, Demirci AM (2023) New soft set operation: Complementary soft binary piecewise star operation. Ikonion Journal of Mathematics 5(2):24-52.
  • Sezgin A, Yavuz E (2023) New soft set operation: Complementary Soft Binary Piecewise Lambda Operation. Sinop University Journal of Natural Sciences 8(2):101-133.
  • Sezgin A, Yavuz E (2023) A new soft set operation: Soft binary piecewise symmetric difference operation. Necmettin Erbakan University Journal of Science and Engineering 5(2):150-168.
  • Sezgin A, Çağman N (2024) New soft set operation: Complementary soft binary piecewise difference operation. Osmaniye Korkut Ata Üniv Fen Biliml Derg 7(1):58-94.
  • Çağman N, Enginoğlu S (2010) Soft set theory and uni-int decision making. Eur J Oper Res 7(2):848-855.
  • Çağman N, Çitak F, Aktaş H (2012) Soft int-group and its applications to group theory. Neural Comput Appl 2:151–158.
  • Sezer AS, Çağman N, Atagün AO, Ali MI, Türkmen E (2015) Soft intersection semigroups, ideals and bi-ideals; a new application on semigroup theory I. Filomat 29(5):917-946.
  • Sezer AS, Çağman N, Atagün AO (2014) Soft intersection interior ideals, quasi-ideals and generalized bi-ideals; a new approach to semigroup theory II. J Mult.-Valued Log. Soft Comput 23(1-2): 161-207.
  • Sezgin A, Orbay M (2022) Analysis of semigroups with soft intersection ideals. Acta Univ Sapientiae Math 14(1):166-210.
  • Mahmood T, Rehman ZU, Sezgin A (2018) Lattice ordered soft near rings. Korean J Math 26(3):503-517.
  • Jana C, Pal M, Karaaslan F, Sezgin A (2019) (α, β)-soft intersectional rings and ideals with their applications. New Math Nat Comput 15(2):333–350.
  • Muştuoğlu E, Sezgin A, Türk ZK (2016) Some characterizations on soft uni-groups and normal soft uni-groups. Int J Comput Appl 155(10):1-8.
  • Sezer AS, Çağman N, Atagün AO (2015) Uni-soft substructures of groups. Ann Fuzzy Math Inform 9(2):235–246.
  • Sezer AS (2014) Certain Characterizations of LA-semigroups by soft sets. J Intell Fuzzy Syst 27(2):1035-1046.
  • Özlü Ş, Sezgin A (2020) Soft covered ideals in semigroups. Acta Univ Sapientiae Math 12(2):317-346.
  • Atagün AO, Sezgin A (2018) Soft subnear-rings, soft ideals and soft n-subgroups of near-rings. Math Sci Letters 7(1):37-42.
  • Sezgin A (2018) A new view on AG-groupoid theory via soft sets for uncertainty modeling. Filomat 32(8):2995–3030.
  • Sezgin A, Çağman N, Atagün AO (2017) A completely new view to soft intersection rings via soft uni-int product. Appl Soft Comput 54:366-392.
  • Sezgin A, Atagün AO, Çağman N, Demir H (2022) On near-rings with soft union ideals and applications. New Math Nat Comput 18(2):495-511.
  • Sezgin A, Çalışıcı H (2024) A comprehensive study on soft binary piecewise difference operation. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B – Teorik Bilimler 12(1):32-54.
  • Sezgin A, Dagtoros K (2023) Complementary soft binary piecewise symmetric difference operation: A novel soft set operation. Scientific Journal of Mehmet Akif Ersoy University 6(2):31-45.
  • Rao MMK (2018) Bi-interior ideals of semigroups. Discuss Mat Gen Algebra Appls 38:69–78.
  • Rao MMK (2018) A study of a generalization of bi-ideal, quasi ideal and interior ideal of semigroup. Mathematica Moravica 22:103–115.
  • Rao MMK (2020) Left bi-quasi ideals of semigroups. Southeast Asian Bull Mat 44:369–376.
  • Rao MMK (2020) Quasi-interior ideals and weak-interior ideals. Asia Pac Journal Mat 7(21):1-20.
  • Baupradist S, Chemat B, Palanivel K, Chinram R (2021) Essential ideals and essential fuzzy ideals in semigroups. J. Discrete Math. Sci. Cryptogr 24(1):223-233.
  • Sezgin A, İlgin A (2024) Soft intersection almost subsemigroups of semigroups, Int. J. Math. Phys. 14(1): in press.
  • Pant S, Dagtoros K, Kholil MI, Vivas A (2024) Matrices: Peculiar determinant property. OPS Journal 1:1–7.

Yarıgrupların esnek kesişimsel hemen hemen idealleri

Yıl 2024, Cilt: 4 Sayı: 2, 466 – 481, 31.07.2024

Aslıhan Sezgin Aleyna İlgin

https://doi.org/10.61112/jiens.1464344

Öz

Bu çalışmanın amacı, bir yarıgrubun boş esnek kümeden farklı esnek kesişimsel sol (sırasıyla sağ) idealinin bir genellemesi olan esnek kesişimsel hemen hemen sol (sırasıyla sağ) ideali kavramını sunmak ve ilgili özellikleri ayrıntılı olarak araştırmaktır. Her idempotent esnek kesişimsel hemen hemen (sol/sağ) idealin, esnek kesişimsel hemen hemen alt yarıgrup olduğu gösterilmiştir. Ayrıca, bir yarıgrubun hemen hemen sol (sırasıyla sağ) idealleri ile esnek kesişimsel hemen hemen sol (sırasıyla sağ) idealleri arasında minimallik, asallık, yarı asallık ve güçlü asallık açısından dikkate değer ilişkiler elde edilmiştir.

Anahtar Kelimeler

esnek küme, yarıgrup, hemen hemen (sağ/sol) idealler, esnek kesişimsel hemen hemen (sağ/sol) idealler

Proje Numarası

YOK

Kaynakça

  • Grosek O, Satko L (1980) A new notion in the theory of semigroup. Semigroup Forum 20: 233–240.
  • Bogdanovic S (1981) Semigroups in which some bi-ideal is a group. Univ u Novom Sadu Zb Rad Prirod Mat Fak Ser Mat 11:261–266.
  • Wattanatripop K, Chinram R, Changphas T (2018) Quasi-A-ideals and fuzzy A-ideals in semigroups. J Discrete Math Sci Cryptogr 21:1131–1138.
  • Kaopusek N, Kaewnoi T, Chinram R (2020) On almost interior ideals and weakly almost interior ideals of semigroups. J Discrete Math Sci Cryptogr 23:773–778.
  • Iampan A, Chinram R, Petchkaew P (2021) A note on almost subsemigroups of semigroups. Int J Math Comput Sci 16 (4):1623–1629.
  • Chinram R, Nakkhasen W (2022) Almost bi-quasi-interior ideals and fuzzy almost bi-quasi-interior ideals of semigroups. J Math Comput Sci 26:128–136.
  • Gaketem T (2021) Almost bi-interior ideal in semigroups and their fuzzifications. Eur J Pure Appl Math 15 (1):281-289.
  • Wattanatripop K, Chinram R, Changphas T (2018) Fuzzy almost bi-ideals in semigroups. Int J Math Comput Sci 13:51–58.
  • Krailoet W, Simuen A, Chinram R, Petchkaew P (2021) A note on fuzzy almost interior ideals in semigroups. Int J Math Comput Sci 16:803–808.
  • Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37(1):19-31.
  • Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(1):555-562.
  • Pei D, Miao D (2005) From soft sets to information systems. In: Proceedings of Granular Computing. IEEE 2:617-621.
  • Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547-1553.
  • Sezgin A, Atagün AO (2011) On operations of soft sets. Comput Math App l61(5):1457-1467.
  • Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56(10):2621-2628.
  • Ali MI, Shabir M, Naz M (2011) Algebraic structures of soft sets associated with new operations. Comput Math Appl 6:2647–2654.
  • Sezgin A, Shahzad A, Mehmood A (2019) New operation on soft sets: Extended difference of soft sets. J New Theory 27:33-42.
  • Stojanovic NS (2021) A new operation on soft sets: Extended symmetric difference of soft sets. Military Technical Courier 69(4):779-791.
  • Sezgin A, Atagün AO (2023) New soft set operation: Complementary soft binary piecewise plus operation. Matrix Science Mathematic 7(2):125-142.
  • Sezgin A, Aybek FN (2023) New soft set operation: Complementary soft binary piecewise gamma operation. Matrix Science Mathematic 7(1):27-45.
  • Sezgin A, Aybek FN, Atagün AO (2023) New soft set operation: Complementary soft binary piecewise intersection operation. BSJ Eng Sci 6(4):330-346.
  • Sezgin A, Aybek FN, Güngör NB (2023) New soft set operation: Complementary soft binary piecewise union operation. Acta Informatica Malaysia 7(1): 38-53.
  • Sezgin A, Demirci AM (2023) New soft set operation: Complementary soft binary piecewise star operation. Ikonion Journal of Mathematics 5(2):24-52.
  • Sezgin A, Yavuz E (2023) New soft set operation: Complementary Soft Binary Piecewise Lambda Operation. Sinop University Journal of Natural Sciences 8(2):101-133.
  • Sezgin A, Yavuz E (2023) A new soft set operation: Soft binary piecewise symmetric difference operation. Necmettin Erbakan University Journal of Science and Engineering 5(2):150-168.
  • Sezgin A, Çağman N (2024) New soft set operation: Complementary soft binary piecewise difference operation. Osmaniye Korkut Ata Üniv Fen Biliml Derg 7(1):58-94.
  • Çağman N, Enginoğlu S (2010) Soft set theory and uni-int decision making. Eur J Oper Res 7(2):848-855.
  • Çağman N, Çitak F, Aktaş H (2012) Soft int-group and its applications to group theory. Neural Comput Appl 2:151–158.
  • Sezer AS, Çağman N, Atagün AO, Ali MI, Türkmen E (2015) Soft intersection semigroups, ideals and bi-ideals; a new application on semigroup theory I. Filomat 29(5):917-946.
  • Sezer AS, Çağman N, Atagün AO (2014) Soft intersection interior ideals, quasi-ideals and generalized bi-ideals; a new approach to semigroup theory II. J Mult.-Valued Log. Soft Comput 23(1-2): 161-207.
  • Sezgin A, Orbay M (2022) Analysis of semigroups with soft intersection ideals. Acta Univ Sapientiae Math 14(1):166-210.
  • Mahmood T, Rehman ZU, Sezgin A (2018) Lattice ordered soft near rings. Korean J Math 26(3):503-517.
  • Jana C, Pal M, Karaaslan F, Sezgin A (2019) (α, β)-soft intersectional rings and ideals with their applications. New Math Nat Comput 15(2):333–350.
  • Muştuoğlu E, Sezgin A, Türk ZK (2016) Some characterizations on soft uni-groups and normal soft uni-groups. Int J Comput Appl 155(10):1-8.
  • Sezer AS, Çağman N, Atagün AO (2015) Uni-soft substructures of groups. Ann Fuzzy Math Inform 9(2):235–246.
  • Sezer AS (2014) Certain Characterizations of LA-semigroups by soft sets. J Intell Fuzzy Syst 27(2):1035-1046.
  • Özlü Ş, Sezgin A (2020) Soft covered ideals in semigroups. Acta Univ Sapientiae Math 12(2):317-346.
  • Atagün AO, Sezgin A (2018) Soft subnear-rings, soft ideals and soft n-subgroups of near-rings. Math Sci Letters 7(1):37-42.
  • Sezgin A (2018) A new view on AG-groupoid theory via soft sets for uncertainty modeling. Filomat 32(8):2995–3030.
  • Sezgin A, Çağman N, Atagün AO (2017) A completely new view to soft intersection rings via soft uni-int product. Appl Soft Comput 54:366-392.
  • Sezgin A, Atagün AO, Çağman N, Demir H (2022) On near-rings with soft union ideals and applications. New Math Nat Comput 18(2):495-511.
  • Sezgin A, Çalışıcı H (2024) A comprehensive study on soft binary piecewise difference operation. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B – Teorik Bilimler 12(1):32-54.
  • Sezgin A, Dagtoros K (2023) Complementary soft binary piecewise symmetric difference operation: A novel soft set operation. Scientific Journal of Mehmet Akif Ersoy University 6(2):31-45.
  • Rao MMK (2018) Bi-interior ideals of semigroups. Discuss Mat Gen Algebra Appls 38:69–78.
  • Rao MMK (2018) A study of a generalization of bi-ideal, quasi ideal and interior ideal of semigroup. Mathematica Moravica 22:103–115.
  • Rao MMK (2020) Left bi-quasi ideals of semigroups. Southeast Asian Bull Mat 44:369–376.
  • Rao MMK (2020) Quasi-interior ideals and weak-interior ideals. Asia Pac Journal Mat 7(21):1-20.
  • Baupradist S, Chemat B, Palanivel K, Chinram R (2021) Essential ideals and essential fuzzy ideals in semigroups. J. Discrete Math. Sci. Cryptogr 24(1):223-233.
  • Sezgin A, İlgin A (2024) Soft intersection almost subsemigroups of semigroups, Int. J. Math. Phys. 14(1): in press.
  • Pant S, Dagtoros K, Kholil MI, Vivas A (2024) Matrices: Peculiar determinant property. OPS Journal 1:1–7.

Toplam 50 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Aktif Algılama
BölümAraştırma Makaleleri
Yazarlar

Aslıhan Sezgin Amasya University 0000-0002-1519-7294 Türkiye

Aleyna İlgin AMASYA ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ 0009-0001-5641-5462 Türkiye

Proje NumarasıYOK
Yayımlanma Tarihi31 Temmuz 2024
Gönderilme Tarihi3 Nisan 2024
Kabul Tarihi21 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 4 Sayı: 2

Kaynak Göster

APASezgin, A., & İlgin, A. (2024). Soft intersection almost ideals of semigroups. Journal of Innovative Engineering and Natural Science, 4(2), 466-481. https://doi.org/10.61112/jiens.1464344

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