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Ashok Khubchandani, Jyoti, Khanderao Nimbhorkar, Shriram. (1399). (a, b)-Fuzzy subrings and (a, b)-fuzzy ideals of a ring. سامانه مدیریت نشریات علمی, 9(2), 96-114. doi: 10.22098/jhs.2020.2633
Jyoti Ashok Khubchandani; Shriram Khanderao Nimbhorkar. "(a, b)-Fuzzy subrings and (a, b)-fuzzy ideals of a ring". سامانه مدیریت نشریات علمی, 9, 2, 1399, 96-114. doi: 10.22098/jhs.2020.2633
Ashok Khubchandani, Jyoti, Khanderao Nimbhorkar, Shriram. (1399). '(a, b)-Fuzzy subrings and (a, b)-fuzzy ideals of a ring', سامانه مدیریت نشریات علمی, 9(2), pp. 96-114. doi: 10.22098/jhs.2020.2633
Ashok Khubchandani, Jyoti, Khanderao Nimbhorkar, Shriram. (a, b)-Fuzzy subrings and (a, b)-fuzzy ideals of a ring. سامانه مدیریت نشریات علمی, 1399; 9(2): 96-114. doi: 10.22098/jhs.2020.2633

(a, b)-Fuzzy subrings and (a, b)-fuzzy ideals of a ring

Journal of Hyperstructures
دوره 9، شماره 2، اسفند 2020، صفحه 96-114    اصل مقاله (291.58 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22098/jhs.2020.2633
نویسندگان
Jyoti Ashok Khubchandani* 1؛ Shriram Khanderao Nimbhorkar2
1Department of Mathematics, Dr.Vitthalrao Vikhe Patil College of Engineering,Ahmednagar 414001, India
2Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India
چکیده
As an extension of the concept of a fuzzy subring and a fuzzy ideal, a new kind of a fuzzy subring and a fuzzy ideal called
an (a, b)-fuzzy subring and an (a, b)-fuzzy ideal of a ring is defined and their properties are studied. We also investigate the preimage of an (a, b)-fuzzy subring and an (a, b)-fuzzy ideal under a ring homomorphism. Also, (a, b)-level fuzzy subrings (fuzzy ideals) are studied. A necessary and sufficient condition for two (a, b)-level fuzzy subrings (fuzzy ideals) to be equal is proved. We show that the set of cosets of an (a, b)-fuzzy ideal forms a ring.
کلیدواژه‌ها
b)-fuzzy subring؛ b)-fuzzy ideal؛ (a؛ b)-fuzzy level subset
مراجع
[1] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[2] J. N. Moderson and D. S. Malik, Fuzzy commutative algebra, World Scienti c, River Edge, NJ, USA, 1998.
[3] L. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
[4] P. K. Sharma,  -Fuzzy subgroups, Inter. J. Fuzzy Math. and Systems, 3(1) (2013), 47-59.
[5] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982), 133-139.

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