Fuzzy ideals of a gamma semiring

Sharma, Tilak Raj; Sharma, Ritu; Sharma, Anuj Kumar

doi:10.1063/5.0095244

Cited by 2 publications

(6 citation statements)

References 6 publications

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“…For the definitions of a Γ−semiring and their identity elements 0 and 1, strong identity, simple, set of units (𝑈 (ΓR)), multiplicative cancellative, Γ−semifield, centreless and additive idempotent, one can refer to (2,6,7) . Now we include some necessary preliminaries for the sake of completeness.…”

Section: Preliminariesmentioning

confidence: 99%

Difference Ordered G􀀀 Semirings

Sharma,

Kumar

2024

IJST

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Objectives: In this study, we generalize some of the difference ordered and weak uniquely difference ordered semirings results. Methods: To establish the results in semirings, we use conditions like commutativity, simple, multiplicative cancellative, additively idempotent on difference-ordered, and weak uniquely difference-ordered semirings. Findings: First, we give some examples of difference ordered semiring, and weak difference ordered semirings. Then generalize some of the results of semirings to semirings and discuss some of the properties of additive idempotent semifield. Novelty: We find that if is a non-zeroic difference ordered semiring then is a strong ideal of Let be a positive difference ordered Gel’fand semiring then every maximal non-unit of is prime. Further, we find that if is a simple difference ordered additively idempotent semiring and which is not a unit then is prime if and only if there exists a character : satisfying Moreover, if and are distinct prime elements of Then and are also distinct. Finally, we consider some properties of additive idempotent semifield and then introduce the concept of weak uniquely difference-ordered semirings. AMS Mathematics subject classification (2020): 16Y60. Keywords: Γ-semiring, Difference ordered Γ-semiring, Additively idempotent Γ- semiring, Strong identity, Weak uniquely difference-ordered Γ-semirings

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Section: Preliminariesmentioning

confidence: 99%

Difference Ordered G􀀀 Semirings

Sharma,

Kumar

2024

IJST

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“…Definition 2.1. (7) Let S and Γ be non-empty sets. Then S is called a Γ− semigroup if there exists a mapping S × Γ × S → S denoted by (x, α, y) → xαy satisfying the condition xα(yβ z) = (xαy)β z for all x, y, z ∈ S and for all α, β ∈ Γ.…”

Section: Preliminaries and Examplesmentioning

confidence: 99%

“…Definition 2.2. (7) Let (R, +) and (Γ, +) be two commutative semigroups. Then R is called a Γ− semiring if there exists a mapping R × Γ × R → R denoted by xαy for all x, y ∈ R and α ∈ Γ satisfying the following condition:…”

Section: Preliminaries and Examplesmentioning

confidence: 99%

“…Definition 2.5. (7) A Γ− semiring R is said to have zero element if 0αx = 0= xα0 and x + 0 = x = 0 + x for all x ∈ R and α ∈ Γ.…”

Section: Preliminaries and Examplesmentioning

confidence: 99%

“…Definition 2.6. (7) A Γ− semiring R is said to have identity element if for all x ∈ R there exist α ∈ Γ such that 1αx = x = xα1. Definition 2.7.…”

Section: Preliminaries and Examplesmentioning

confidence: 99%

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Prime Fuzzy Ideals of a Gamma Semiring -1

Sharma,

Sharma

2023

IJST

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Objectives:The main objective of this article is to introduce some fundamental results of fuzzy ideals and Prime fuzzy ideals of a Γ− semiring R . Methods: We use some fundamental results of fuzzy ideals and conditions like semi subtractive, centreless etc. for developments of the main results. Findings: In this connection, we establish some important results of fuzzy ideals and prime fuzzy ideals of semirings to Γ− semirings. Novelty: We find a special class of fuzzy ideals of a Γ− semiring R and with this, construct a lattice ordered Γ− semiring. Further, we find that a fuzzy ideal of Γ− semiring R can be a decreasing map from [0, 1] into the set of R together with an empty set. As an application of this result, the prime fuzzy ideals of a Γ− semiring R are described in terms of prime ideals of a Γ− semiring R.

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Fuzzy ideals of a gamma semiring

Cited by 2 publications

References 6 publications

Difference Ordered G􀀀 Semirings

Difference Ordered G􀀀 Semirings

Prime Fuzzy Ideals of a Gamma Semiring -1

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