Results of fuzzy prime near-rings with fuzzy involutions

M. Ou-Mha; A. Raji; M. Oukessou

doi:10.5269/bspm.77959

M. Ou-Mha Sultan Moulay Slimane University
A. Raji
M. Oukessou

Abstract

The main objective of this paper is to introduce the concept of fuzzy involution on fuzzy nearrings, and we prove that a fuzzy near-ring satisfying certain identities involving fuzzy involution must be a fuzzy ring or a commutative fuzzy ring. Also, an example proving the existence of this type of mapping is given.

Downloads

Download data is not yet available.

References

H. Aktas and N. Çagman, A type of fuzzy ring, Arch. Math. Logic 46, 165-177, (2007).

A. Boua and A. Raji, Several algebraic inequalities on a 3-prime near-ring, JP J. Algebra Number Theory Appl. 39 (1), 105–113, (2017).

L. Oukhtite and A. Raji, On two-sided α-n-derivation in 3-prime near-rings, Acta Math. Hungar. 157 (2), 465-477, (2019).

N. Olgun, Direct Product of Fuzzy Groups and Fuzzy Rings, International Mathematical Forum 6(1), 1005-1015, (2011).

M. Ou-mha, A. Raji and M. Oukessou, A study of the fuzzy multiplicative center in a special class of fuzzy near rings, Bol. Soc. Paran. Mat. 43, 1-9, (2025).

M. Ou-mha, A. Raji, M. Oukessou and A. Boua, A study of fuzzy prime near-rings involving fuzzy semigroup ideals, Wseas Transactions on Mathematics 23, 392-399, (2024).

M. A. Öztürk, Y. B. Jun and H. Yazarh, A new view of fuzzy gamma rings, Hacet. J. Math. Stat. 39 (3), 365-378, (2010).

A. Raji, On multiplicative derivations in 3-prime near-rings, Beitr. Algebra Geom. 65 (2), 343-357, (2024).

A. Raji, M. Oukessou and A. Belharrate, Semigroup ideals with multiplicative semiderivations and commutativity of 3-prime near-rings, Note Mat. 42 (2), 43-52, (2022).

A. Raji, M. Oukessou and A. Belharrate, Jordan ideals with multiplicative derivations in 3-prime near-rings, Adv. Math. Models Appl. 7 (2), 214-222, (2022).

A. Raji, Some commutativity criteria for 3-prime near-rings, Algebra Discrete Math. 32 (2), 280-298, (2021).

E. Ranjbar-Yanehsari and M. Asghari-Larimi, A New View of Fuzzy Vector Space Over Fuzzy Field, Jordan J. Math. Stat. 11 (3), 193-210, (2018).

E. Yetkin and N. Olgun, A New Type Fuzzy Module over Fuzzy Rings, The Scientific World Journal, Volume 2014, Article ID 730932, 7 pages.

X. Yuan, The Category FGrp of Fuzzy Groups Is Not Equivalent to the Category Grp of Classical Groups, Computers and Mathematics with Apphcations 49, 1953-1956, (2005).

X. Yuan and E. S. Lee, Fuzzy group based on fuzzy binary operation, Comput. Math. App. 47, 631-641, (2004).