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On 1-Absorbing Fuzzy Ideals of Commutative Semirings

Yıl 2023, Cilt: 8 Sayı: 3, 131 - 141, 31.12.2023
https://doi.org/10.30931/jetas.1302897

Öz

In this study, the algebraic structure of 1-absorbing ideals is first examined and applied to fuzzy sets, along with an investigation into the relationships and algebraic properties between them. The contribution to this work's literature involves examining 1-absorbing fuzzy primary ideals. Features of 1-absorbing fuzzy primary ideals are explored, and it is demonstrated, for instance, that I is deemed a 1-absorbing fuzzy primary ideal of P if I is a fuzzy primary ideal of P. Additionally, I is considered a 2-absorbing fuzzy primary ideal of P if I is a 1-absorbing fuzzy primary ideal of P. Furthermore, these theorems are elucidated through specific examples.

Destekleyen Kurum

Research Fund of the Yildiz Technical University

Proje Numarası

FYL-2022-5038

Kaynakça

  • [1] Atani, R. E., and Atani, S. E., “Ideal theory in commutative semirings”, Buletinul Academiei de Stiinte a Republicii Moldova Matematica 2 (2008) : 14-23.
  • [2] Zadeh, L.A., “Fuzzy sets”, Inform. and Control 8 (1965) : 338-353.
  • [3] Roberts, D. W., “Ordination based on fuzzy set theory”, Vegetation 66(3) (1986) : 123-131.
  • [4] Zimmermann, H. J., “Fuzzy set theory”, Wiley interdisciplinary reviews: Computational statistics 2(3) (2010) : 317-332.
  • [5] Chang, C. L., “Fuzzy topological spaces”, Journal of Mathematical Analysis and Applications 24(1) (1968) : 182-190.
  • [6] Rosenfeld, A., “Fuzzy groups”, Journal of Mathematical Analysis and applications 35(3) (1971) : 512-517.
  • [7] Liu, W. J., “Fuzzy invariant subgroups and fuzzy ideals”, Fuzzy sets and Systems 8(2) (1982) : 133-139.
  • [8] Abou-Zaid, S., “On fuzzy subnear-rings and ideals”, Fuzzy sets and systems 44(1) (1991) : 139-146.
  • [9] Atanassov, K. T., “Intuitionistic fuzzy sets. In Intuitionistic fuzzy sets”, Physica, Heidelberg (1999) : 1-137.
  • [10] Szmidt, E., and Kacprzyk, J., “Distances between intuitionistic fuzzy sets”, Fuzzy sets and systems 114(3) (2000) : 505-518.
  • [11] Özdemir, O., & Kalınkara, Y., “Bulanık Mantık: 2000-2020 Yılları Arası Tez ve Makale Çalışmalarına Yönelik Bir İçerik Analizi”, Acta Infologica 4(2) (2020) : 155-174.
  • [12] Badawi, A., “On 2-absorbing ideals of commutative rings”, Bulletin of the Australian Mathematical Society 75(3) (2007) : 417-429.
  • [13] Badawi, A., & Celikel, E. Y., “On 1-absorbing primary ideals of commutative rings”, Journal of Algebra and Its Applications 19(06) (2020) : 2050111.
  • [14] Yassine, A., Nikmehr, M. J., & Nikandish, R., “On 1-absorbing prime ideals of commutative rings”, Journal of Algebra and its Applications 20(10) (2021): 2150175.
  • [15] Mandal, D., “On 2-absorbing fuzzy ideals of commutative semirings”, TWMS Journal of Applied and Engineering Mathematics 11(2) (2021) : 368.
  • [16] Darani, A.Y., Hashempoor, A., “L-fuzzy 0-(1-or 2-or 3-) 2-absorbing ideals in semiring”, Ann. Fuzzy Math. Inform. 7 (2014) : 303-311.
  • [17] Jonathan S. Golan, “Semirings and their applications”, Springer (2013) : 105-120.
  • [18] Darani, Ahmad Yousefian, “On 2-absorbing and weakly 2-absorbing ideals of commutative semirings”, Kyungpook Mathematical Journal 52 (1) (2012) : 91-97.
  • [19] Chaudhari, Jayprakash Ninu, “2-absorbing ideals in semirings”, International Journal of Al- gebra 6 (6) (2012) : 265-270.
  • [20] Groenewald, Nico, “On weakly 2-absorbing ideals of non-commutative rings”, Afrika Matematika 32(7-8) (2021) : 1669-1683.
  • [21] Soheilnia, Fatemeh, “On 2-absorbing and weakly 2-absorbing primary ideals of a commutative semiring”, Kyungpook Mathematical Journal 56 (1) (2016).
  • [22] Behzadipour, Hussein, and Peyman Nasehpour, “On 2-absorbing ideals of commutative semir- ings”, Journal of Algebra and Its Applications 19 (2)(2020) : 2050034.
  • [23] Jaber, Ameer., “Properties of weakly 2-absorbing primal ideals”, Italian Journal of Pure and Applied Mathematics 7 (2022) : 609-619.
  • [24] Groenewald, N. J., “On 2-absorbing and weakly 2-absorbing principally right primary ideals”, Journal of Algebra and Related Topics 9 (2) (2021) : 47-67.
  • [25] Sahoo, Taptee, Deepak Shetty, M., Groenewald, N. J., Harikrishnan, P. K., Kuncham, S. P., “On completely 2-absorbing ideals of N-groups”, Journal of Discrete Mathematical Sciences and Cryptography 24 (2) (2021) : 541-556.
  • [26] Yassine, A., M. J. Nikmehr, and R. Nikandish., “On 1-absorbing prime ideals of commutative rings”, Journal of Algebra and its Applications 20(10) (2021) : 2150175.
  • [27] Koc, Suat, Ünsal Tekir, and Eda Yıldız, “On weakly 1-absorbing prime ideals”, Ricerche di Matematica 72(2) (2023) : 723-738.
  • [28] Groenewald, Nico., “1-absorbing prime ideals and weakly 1-absorbing prime ideals in non-commutative rings”, S˜ao Paulo Journal of Mathematical Sciences (2022) : 1-17.
  • [29] Bouba, E. M., Tamekkante, M., Tekir, U¨ ., and Ko¸c, S., “Notes on 1-absorbing prime ideals”,Proceedings of the Bulgarian Academy of Sciences 75(5) (2022) : 631-639.
  • [30] Abu-Dawwas, R., Yıldız, E., Tekir, U¨ ., Koc, S., “On graded 1-absorbing prime ideals.” Sao Paulo Journal of Mathematical Sciences 15 (2021) : 450-462.
  • [31] Anbarloei, Mahdi., “On 1-absorbing prime hyperideal and some of its generalizations”, Journal of Mathematics (2022) : 4947019.
  • [32] Saleh, Mohammad, and Ibaa M., “On weakly 1-absorbing primary ideals of commutative semirings”, Communications in Advanced Mathematical Sciences 5(4) (2022) : 199-208.
Yıl 2023, Cilt: 8 Sayı: 3, 131 - 141, 31.12.2023
https://doi.org/10.30931/jetas.1302897

Öz

Proje Numarası

FYL-2022-5038

Kaynakça

  • [1] Atani, R. E., and Atani, S. E., “Ideal theory in commutative semirings”, Buletinul Academiei de Stiinte a Republicii Moldova Matematica 2 (2008) : 14-23.
  • [2] Zadeh, L.A., “Fuzzy sets”, Inform. and Control 8 (1965) : 338-353.
  • [3] Roberts, D. W., “Ordination based on fuzzy set theory”, Vegetation 66(3) (1986) : 123-131.
  • [4] Zimmermann, H. J., “Fuzzy set theory”, Wiley interdisciplinary reviews: Computational statistics 2(3) (2010) : 317-332.
  • [5] Chang, C. L., “Fuzzy topological spaces”, Journal of Mathematical Analysis and Applications 24(1) (1968) : 182-190.
  • [6] Rosenfeld, A., “Fuzzy groups”, Journal of Mathematical Analysis and applications 35(3) (1971) : 512-517.
  • [7] Liu, W. J., “Fuzzy invariant subgroups and fuzzy ideals”, Fuzzy sets and Systems 8(2) (1982) : 133-139.
  • [8] Abou-Zaid, S., “On fuzzy subnear-rings and ideals”, Fuzzy sets and systems 44(1) (1991) : 139-146.
  • [9] Atanassov, K. T., “Intuitionistic fuzzy sets. In Intuitionistic fuzzy sets”, Physica, Heidelberg (1999) : 1-137.
  • [10] Szmidt, E., and Kacprzyk, J., “Distances between intuitionistic fuzzy sets”, Fuzzy sets and systems 114(3) (2000) : 505-518.
  • [11] Özdemir, O., & Kalınkara, Y., “Bulanık Mantık: 2000-2020 Yılları Arası Tez ve Makale Çalışmalarına Yönelik Bir İçerik Analizi”, Acta Infologica 4(2) (2020) : 155-174.
  • [12] Badawi, A., “On 2-absorbing ideals of commutative rings”, Bulletin of the Australian Mathematical Society 75(3) (2007) : 417-429.
  • [13] Badawi, A., & Celikel, E. Y., “On 1-absorbing primary ideals of commutative rings”, Journal of Algebra and Its Applications 19(06) (2020) : 2050111.
  • [14] Yassine, A., Nikmehr, M. J., & Nikandish, R., “On 1-absorbing prime ideals of commutative rings”, Journal of Algebra and its Applications 20(10) (2021): 2150175.
  • [15] Mandal, D., “On 2-absorbing fuzzy ideals of commutative semirings”, TWMS Journal of Applied and Engineering Mathematics 11(2) (2021) : 368.
  • [16] Darani, A.Y., Hashempoor, A., “L-fuzzy 0-(1-or 2-or 3-) 2-absorbing ideals in semiring”, Ann. Fuzzy Math. Inform. 7 (2014) : 303-311.
  • [17] Jonathan S. Golan, “Semirings and their applications”, Springer (2013) : 105-120.
  • [18] Darani, Ahmad Yousefian, “On 2-absorbing and weakly 2-absorbing ideals of commutative semirings”, Kyungpook Mathematical Journal 52 (1) (2012) : 91-97.
  • [19] Chaudhari, Jayprakash Ninu, “2-absorbing ideals in semirings”, International Journal of Al- gebra 6 (6) (2012) : 265-270.
  • [20] Groenewald, Nico, “On weakly 2-absorbing ideals of non-commutative rings”, Afrika Matematika 32(7-8) (2021) : 1669-1683.
  • [21] Soheilnia, Fatemeh, “On 2-absorbing and weakly 2-absorbing primary ideals of a commutative semiring”, Kyungpook Mathematical Journal 56 (1) (2016).
  • [22] Behzadipour, Hussein, and Peyman Nasehpour, “On 2-absorbing ideals of commutative semir- ings”, Journal of Algebra and Its Applications 19 (2)(2020) : 2050034.
  • [23] Jaber, Ameer., “Properties of weakly 2-absorbing primal ideals”, Italian Journal of Pure and Applied Mathematics 7 (2022) : 609-619.
  • [24] Groenewald, N. J., “On 2-absorbing and weakly 2-absorbing principally right primary ideals”, Journal of Algebra and Related Topics 9 (2) (2021) : 47-67.
  • [25] Sahoo, Taptee, Deepak Shetty, M., Groenewald, N. J., Harikrishnan, P. K., Kuncham, S. P., “On completely 2-absorbing ideals of N-groups”, Journal of Discrete Mathematical Sciences and Cryptography 24 (2) (2021) : 541-556.
  • [26] Yassine, A., M. J. Nikmehr, and R. Nikandish., “On 1-absorbing prime ideals of commutative rings”, Journal of Algebra and its Applications 20(10) (2021) : 2150175.
  • [27] Koc, Suat, Ünsal Tekir, and Eda Yıldız, “On weakly 1-absorbing prime ideals”, Ricerche di Matematica 72(2) (2023) : 723-738.
  • [28] Groenewald, Nico., “1-absorbing prime ideals and weakly 1-absorbing prime ideals in non-commutative rings”, S˜ao Paulo Journal of Mathematical Sciences (2022) : 1-17.
  • [29] Bouba, E. M., Tamekkante, M., Tekir, U¨ ., and Ko¸c, S., “Notes on 1-absorbing prime ideals”,Proceedings of the Bulgarian Academy of Sciences 75(5) (2022) : 631-639.
  • [30] Abu-Dawwas, R., Yıldız, E., Tekir, U¨ ., Koc, S., “On graded 1-absorbing prime ideals.” Sao Paulo Journal of Mathematical Sciences 15 (2021) : 450-462.
  • [31] Anbarloei, Mahdi., “On 1-absorbing prime hyperideal and some of its generalizations”, Journal of Mathematics (2022) : 4947019.
  • [32] Saleh, Mohammad, and Ibaa M., “On weakly 1-absorbing primary ideals of commutative semirings”, Communications in Advanced Mathematical Sciences 5(4) (2022) : 199-208.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Doç. Dr. Erdoğan Mehmet Özkan 0000-0003-2341-6626

Serkan Onar 0000-0003-3084-7694

Ayten Ozkan 0000-0002-3948-1943

İlayda Kaplan 0000-0002-6198-1573

Proje Numarası FYL-2022-5038
Erken Görünüm Tarihi 30 Aralık 2023
Yayımlanma Tarihi 31 Aralık 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 8 Sayı: 3

Kaynak Göster

APA Mehmet Özkan, D. D. E., Onar, S., Ozkan, A., Kaplan, İ. (2023). On 1-Absorbing Fuzzy Ideals of Commutative Semirings. Journal of Engineering Technology and Applied Sciences, 8(3), 131-141. https://doi.org/10.30931/jetas.1302897
AMA Mehmet Özkan DDE, Onar S, Ozkan A, Kaplan İ. On 1-Absorbing Fuzzy Ideals of Commutative Semirings. JETAS. Aralık 2023;8(3):131-141. doi:10.30931/jetas.1302897
Chicago Mehmet Özkan, Doç. Dr. Erdoğan, Serkan Onar, Ayten Ozkan, ve İlayda Kaplan. “On 1-Absorbing Fuzzy Ideals of Commutative Semirings”. Journal of Engineering Technology and Applied Sciences 8, sy. 3 (Aralık 2023): 131-41. https://doi.org/10.30931/jetas.1302897.
EndNote Mehmet Özkan DDE, Onar S, Ozkan A, Kaplan İ (01 Aralık 2023) On 1-Absorbing Fuzzy Ideals of Commutative Semirings. Journal of Engineering Technology and Applied Sciences 8 3 131–141.
IEEE D. D. E. Mehmet Özkan, S. Onar, A. Ozkan, ve İ. Kaplan, “On 1-Absorbing Fuzzy Ideals of Commutative Semirings”, JETAS, c. 8, sy. 3, ss. 131–141, 2023, doi: 10.30931/jetas.1302897.
ISNAD Mehmet Özkan, Doç. Dr. Erdoğan vd. “On 1-Absorbing Fuzzy Ideals of Commutative Semirings”. Journal of Engineering Technology and Applied Sciences 8/3 (Aralık 2023), 131-141. https://doi.org/10.30931/jetas.1302897.
JAMA Mehmet Özkan DDE, Onar S, Ozkan A, Kaplan İ. On 1-Absorbing Fuzzy Ideals of Commutative Semirings. JETAS. 2023;8:131–141.
MLA Mehmet Özkan, Doç. Dr. Erdoğan vd. “On 1-Absorbing Fuzzy Ideals of Commutative Semirings”. Journal of Engineering Technology and Applied Sciences, c. 8, sy. 3, 2023, ss. 131-4, doi:10.30931/jetas.1302897.
Vancouver Mehmet Özkan DDE, Onar S, Ozkan A, Kaplan İ. On 1-Absorbing Fuzzy Ideals of Commutative Semirings. JETAS. 2023;8(3):131-4.