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Fuzzy subrings and ideals redefined. (English) Zbl 0878.16025

Summary: \((\varepsilon, \varepsilon\vee q)\)-fuzzy subrings and ideals of a ring are defined. The concepts of \((\varepsilon, \varepsilon\vee q)\)-fuzzy semiprime, prime, semiprimary, primary and maximal ideals are introduced and characterization of such fuzzy ideals are obtained. \((\varepsilon, \varepsilon\vee q)\)-fuzzy cosets determined by \((\varepsilon, \varepsilon\vee q)\)-fuzzy ideals and \((\varepsilon, \varepsilon\vee q)\)-fuzzy radicals of \((\varepsilon, \varepsilon\vee q)\)-fuzzy ideals are discussed.

MSC:

16Y99 Generalizations
16D25 Ideals in associative algebras
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[1] Bhakat, S. K.; Das, P., \(q\)-similitudes and \(q\)-fuzzy partitions, Fuzzy Sets and Systems, 51, 195-202 (1992) · Zbl 0783.04004
[2] Bhakat, S. K.; Das, P., On the definition of a fuzzy subgroup, Fuzzy Sets and Systems, 51, 235-241 (1992) · Zbl 0786.20047
[3] Bhakat, S. K.; Das, P., (α, β)-fuzzy mappings, Fuzzy Sets and Systems, 56, 89-95 (1993) · Zbl 0797.04007
[4] Dixit, V. N.; Kumar, R.; Ajmal, N., Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy Sets and Systems, 44, 127-138 (1991) · Zbl 0772.16002
[5] Kumar, R., Fuzzy nil radical and fuzzy primary ideals, Fuzzy Sets and Systems, 43, 81-93 (1991) · Zbl 0761.16002
[6] Kumar, R., Fuzzy semiprimary ideals of rings, Fuzzy Sets and Systems, 42, 263-273 (1991) · Zbl 0745.16001
[7] Kumar, R., Certain fuzzy ideals of rings redefined, Fuzzy Sets and Systems, 46, 257-260 (1992) · Zbl 0772.16001
[8] Kumbhojkar, H. V.; Bapat, M. S., Not-so-fuzzy fuzzy ideals, Fuzzy Sets and Systems, 37, 237-243 (1990) · Zbl 0709.16001
[9] Kambhojkar, H. V.; Bapat, M. S., On prime and primary fuzzy ideals and their radicals, Fuzzy Sets and Systems, 53, 203-216 (1993) · Zbl 0796.16005
[10] Liu, W. J., Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8, 133-139 (1982) · Zbl 0488.20005
[11] Liu, W. J., Operaions on fuzzy ideals, Fuzzy Sets and Systems, 11, 37-41 (1983)
[12] Malik, D. S.; Mordeson, J., Radicals of fuzzy ideals, Inform. Sci, 65, 239-252 (1992) · Zbl 0763.13005
[13] Ming, P. P.; Ming, L. Y., Fuzzy topology I. Neighbourhood structures of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76, 571-579 (1980)
[14] Mukherjee, T. K.; Sen, M., On fuzzy ideals of a ring (1), Fuzzy Sets and Systems, 21, 99-104 (1987) · Zbl 0617.13001
[15] Mukherjee, T. K.; Sen, M., Prime fuzzy ideals in rings, Fuzzy Sets and Systems, 32, 337-341 (1989) · Zbl 0677.16021
[16] Rosenfeld, A., Fuzzy groups, J. Math. Anal. Appl., 35, 512-517 (1971) · Zbl 0194.05501
[17] Sidky, F. I.; Khatab, A. S., Nil radical of fuzzy ideal, Fuzzy Sets and Systems, 47, 117-120 (1992) · Zbl 0770.13017
[18] Zadeh, L. A., Fuzzy Sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606
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