M. Murali Krishna Rao, Noorbhasha Rafi and Rajendra Kumar Kona*
Annals of Communications in Mathematics 2023,
6 (4),
225-237
DOI: https://doi.org/10.62072/acm.2023.060403
AbstractIn this paper, we introduce the notion of a fuzzy soft tri-ideal over Γ−semiring. We characterize the regular Γ−semiring in terms of fuzzy soft tri-ideals, and study some of the properties. M is a regular Γ−semiring, E be a parameters set and A ⊆ E. If (µ, A) is a fuzzy soft left tri-ideal over M, then (µ, A) is a fuzzy soft right ideal over M.
M. Murali Krishna Rao
Annals of Communications in Mathematics 2023,
6 (4),
266-281
DOI: https://doi.org/10.62072/acm.2023.060408
AbstractIn this paper we introduce the notion of anti fuzzy ideals, anti fuzzy k−ideals of ordered semirings and we study the properties of anti fuzzy ideals, anti fuzzy k−ideals, homomorphic and anti homomorphic image and pre-image of fuzzy ideals, anti fuzzy ideals and anti fuzzy k−ideals of an ordered semiring. We characterize the ideals of an ordered semiring in terms of anti fuzzy k−ideals.
M. Murali Krishna Rao* and Noorbhasha Rafi
Annals of Communications in Mathematics 2024,
7 (1),
10-20
DOI: https://doi.org/10.62072/acm.2024.070102
AbstractIn this paper, we introduce the notion of interval valued fuzzy prime ideals of Γ−semirings.We study, some properties of prime ideals of a Γ−semirng in terms of interval valued fuzzy ideals.
M. Murali Krishna Rao
Annals of Communications in Mathematics 2024,
7 (2),
114-127
DOI: https://doi.org/10.62072/acm.2024.070205
AbstractWe introduce the notion of ideal, prime ideal, filter, fuzzy ideal, fuzzy prime ideal, fuzzy filter of an ordered semiring and study their properties and relations between them. We characterize the prime ideals and filters of an ordered semiring with respect to fuzzy ideals and fuzzy filters respectively. We proved a fuzzy subset µ is a fuzzy filter of an ordered semiring M if and only if µMT β, : X → [0, 1] is a fuzzy filter of an ordered semiring M. M and N be ordered semirings and ϕ : M → N be an onto homomorphism. If f is a ϕ homomorphism invariant fuzzy filter of M then ϕ(f) is a fuzzy filter of N.
M. Murali Krishna Rao and Noorbhasha Rafi*
Annals of Communications in Mathematics 2024,
7 (3),
241-251
DOI: https://doi.org/10.62072/acm.2024.070302
AbstractIn this section, we introduce the notions of a left and a right translational invariant fuzzy subsets of a Γ−semigroup M, as well as the concept of a unit with respect to a fuzzy subset, and study their properties. We also prove that if μ is a translational invariant fuzzy subset of a commutative Γ−semigroup with unity, then the principal ideal generated by an element and μ that contains a unity element is a prime ideal of the Γ−semigroup.
M. Murali Krishna Rao and Noorbhasha Rafi*
Annals of Communications in Mathematics 2025,
8 (3),
379-385
DOI: https://doi.org/10.62072/acm.2025.080304
ABSTRACT. In this paper, we introduce the notion of involution in semirings. We define bi-ideal, quasi ideal, interior ideal, bi-quasi interior ideal, and bi-interior ideals of semirings with involution and study their properties.
Ganesh Kumar Reddi, M. Murali Krishna Rao, Rajendra Kumar Kona* and Vineela B
Annals of Communications in Mathematics 2025,
8 (3),
410-424
DOI: https://doi.org/10.62072/acm.2025.080308
ABSTRACT. In this paper, we introduce the notion of a fuzzy bi-quasi interior ideal as a generalization of fuzzy ideals, fuzzy bi-quasi ideals, fuzzy quasi-interior ideals and fuzzy bi-interior ideals of a semiring. We prove that every fuzzy right quasi-interior ideal of a semiring is a fuzzy bi-quasi interior ideal and a fuzzy bi-quasi interior ideal is a fuzzy right tri-ideal of a semiring. We characterize the regular semiring in terms of fuzzy bi-quasi interior ideals and study some of the properties.
Open AccessArticle