Seminearrings, seminearfields and their semigroup-theoretical background

Weinert, Hanns Joachim

doi:10.1007/bf02572770

Cited by 30 publications

(5 citation statements)

References 10 publications

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“…If Γ and Γ are two S-semigroups of a nearsemiring S. A mapping φ : Γ → Γ is said to be an S-morphism between Ssemigroups Γ and Γ if it satisfies: (i) φ(x + y) = φ(x)+ φ(y), (ii) φ(rx) = rφ(x), for all x, y ∈ Γ, r ∈ S and (iii) φ(0 Γ ) = 0 Γ . We refer [31][32][33] for further discussion on nearsemirings and S-semigroups of nearsemirings. Throughout, S represents a nearsemiring, U an initial universe, E the possible parameters associated with the elements in U , ℘(U ) represents the family of subsets of U , S(U ) the collection of soft sets and A = ∅ be a subset of E.…”

Section: Preliminariesmentioning

confidence: 99%

Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Khan

Taouti

2022

IJFIS

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In this note, we introduce and discuss the notions of soft sub-nearsemirings, soft ideals and soft S-subsemigroups of nearsemirings. Some related properties and characterizations of these soft algebraic structures are discussed with illustrative examples. For the sake of investigations, we apply several operations of soft sets including soft intersection sum, soft product and soft uniint product. Based on these operations, we also discuss few characterizations of distributively generated nearsemirings. In due course, we investigate few relationships among these soft algebraic structures and the classical nearsemirings. We also introduce the notion of soft ideals (left and right) of nearsemirings. Firstly, we investigate these ideals by applying few operations on them. Then, we present the relationship between these soft ideals of nearsemiring with the classical ideals of nearsemirings. Moreover, we introduce the notion of soft S-homomorphism between two soft S-subsemigroups and investigate that the homomorphic image of soft S-subsemigroup is a soft S-subsemigroup. Throughout, we shift several substructures of nearsemirings towards the soft algebraic substructures of nearsemirings by utilizing different algebraic methods. Consequently, we explore a linkage among the soft set theory, classical set theory and nearsemiring theory. Mainly, our study is the interplay between soft substructures of nearsemirings and classical substructures of nearsemirings.

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Section: Preliminariesmentioning

confidence: 99%

Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Khan

Taouti

2022

IJFIS

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“…The concept of seminearring was introduced by W. G. van Hoorn et al in [1]. Seminearfields have been introduced in [5]. As a generalization of seminearrings that is Γseminear-rings were introduced in [2].…”

Section: Introductionmentioning

confidence: 99%

Weakly Prime and Weakly Primary Ideals in Gamma Seminearrings

Khan¹,

Taouti

Karkain

et al. 2019

Eur. J. Pure Appl. Math.

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“…Some authors have considered studying the algebraic structure of near-semirings (e.g. Hoogewijs (1976); Krishna and Chatterjee (2007); van Hoorn (1970); Weinert (1982)) and others utilized the concept in various applications (e.g. Desharnais and Struth (2008)).…”

Section: Introductionmentioning

confidence: 99%

Affine Near-Semirings Over Brandt Semigroups

Kumar

Krishna

2014

Communications in Algebra

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Abstract. This work investigates the rank properties of A + (Bn), the additive semigroup reduct of affine near-semiring over Brandt semigroup Bn. In this connection, this work reports the ranks r 1 , r 2 , r 3 and r 5 of A + (Bn) and identifies a lower bound for the upper rank r 4 (A + (Bn)). While this lower bound is found to be the r 4 (A + (Bn)) for n ≥ 6, in other cases where 2 ≤ n ≤ 5, the upper rank of A + (Bn) is still open for investigation.

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Seminearrings, seminearfields and their semigroup-theoretical background

Cited by 30 publications

References 10 publications

Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Weakly Prime and Weakly Primary Ideals in Gamma Seminearrings

Affine Near-Semirings Over Brandt Semigroups

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