Prime Near-rings Research Articles

A Study of Fuzzy Prime Near-rings Involving Fuzzy Semigroup Ideals

In this paper, our main objective is to introduce the notion of a fuzzy semigroup ideal by using Yuan and Lee's definition of fuzzy group based on fuzzy binary operations. Also, some of its basic properties are studied analogously to the known results in the case of semigroup ideals defined in the framework of ordinary near-rings.

Some specific differential identities in 3-prime near-rings

In this paper, we study 3-prime near-rings with left generalized semiderivations that satisfy specific diferential identities. Consequently, some well-known results from the literature have been generalized. We also show how the constraints placed on the hypothesis of various results are really not redundant.

Jordan ideals and $$(\alpha , \beta )$$-derivations on 3-prime near-rings and rings

Jordan ideals and $$(\alpha , \beta )$$-derivations on 3-prime near-rings and rings

Some algebraic identities in 3-prime near-rings

Some algebraic identities in 3-prime near-rings

Commutativity of some Prime Nearrings using Left-Sided outer (σ, τ)-n-Derivation

In the field of mathematics, pure mathematics is very important as it gives rise to the basis for the formation of all applicable mathematical concepts in solving real-life problems. Algebra is such an integral part of pure mathematics. It consists of the Ring theory. It has been discovered that there exists some structures similar to rings with little deformity and they are called NEARRINGS. These structures do not commute mostly as they fail to satisfy distributive law. To ascertain the commutativity of nearrings, we need derivation(s). Because several papers had been presented dealing with left-nearrings, this paper aimed to consider right-nearrings which has not been done before in that respect, to the best of our knowledge. Some methods dealing with left-nearrings have been studied and modified in this work, and new derivation has been introduced to take care of right-nearrings. For Let

Left multipliers and commutativity of 3-prime near-rings

Our objective in this paper is to study the structure of 3-prime near-rings satisfying some algebraic properties.

On Semigroup Ideals and Right n-Derivation in 3-Prime Near-Rings

The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals of near-rings and some related properties. Interesting results have been reached, the most prominent of which are the following: Let M be a 3-prime left near-ring and A_1,A_2,…,A_n are nonzero semigroup ideals of M, if d is a right n-derivation of M satisfies on of the following conditions,d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u;d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=0 ∀u_1,v_1 〖ϵA〗_1,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u ;d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=(u_j,v_j ) ∀ u_1,v_1 〖ϵA〗_1 ,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u;If d+d is an n -additive mapping from A_1×A_2×…×A_n to M;d(u_1,u_2,…,(u_j,v_j ),…,u_n)∈ Z(M) ∀〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u,; d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))∈ Z(M) ∀ u_1,v_1 〖ϵA〗_1 ,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u;Then M is a commutative ring.

On multiplicative derivations in 3-prime near-rings

On multiplicative derivations in 3-prime near-rings

On Jordan ideals with left derivations in 3-prime near-rings

We will extend in this paper some results about commutativity of Jordan ideals proved in [2] and [6]. However, we will consider left derivations instead of derivations, which is enough to get good results in relation to the structure of near-rings. We will also show that the conditions imposed in the paper cannot be removed.

On zero-power valued homoderivations in 3-prime near-rings

We will start this article by proving a crucial concept, which will allow us to overcome a set of obstacles we encountered in previous articles concerning the commutativity of near-ring involving homoderivations and Jordan ideals. Furthermore, we present examples to show that limitations imposed in the hypothesis of our results are necessary.

Generalized (α, β)-derivations in 3-prime near-rings

Let be a 3-prime near-ring and are endomorphisms. In this paper, we generalize a few results concerning generalized derivations and two sided α -generalized derivations of 3-prime near rings to generalized (α, β) -derivations. Cases demonstrating the need of the 3-primeness speculation is given. When (resp. ), one can easily obtain the main results of [1] (resp. [4]).

On two-sided α-generalized derivations of 3-prime near-rings

In the first part of this paper, we mention some errors in Communications in Algebra, DOI:10.1080/00927872.2019.1684510, and give a correct version of the errant results. In the second part, we generalize some results in Communications in Algebra (DOI:10.1080/00927872.2016.1274900) and present our contribution in the study of generalized two-sided α-derivations satisfying certain identities over near-rings.

On commutativity of 3-prime near-rings with generalized (α; β)-derivations

Let \(\mathcal{N}\) be a~\(3\)-prime near ring and \(\alpha,\beta: \mathcal{N}\rightarrow \mathcal{N}\) be endomorphisms. In the present paper we amplify a~few outcomes concerning generalized derivations and two-sided \(\alpha\)-generalized derivations of \(3\)-prime near rings to generalized \((\alpha,\beta)\)-derivations. Cases demonstrating the need of the \(3\)-primeness speculation are given. When \(\beta = id_{\mathcal{N}}\) (resp. \(\alpha = \beta = id_{\mathcal{N}}\)), one can easily obtain the main results of~\cite{ref1} (resp.\cite{ref5}).

On commutativity of 3-prime near-rings with generalized (α; β)-derivations

On commutativity of 3-prime near-rings with generalized (α; β)-derivations

On commutativity of 3-prime near-rings with generalized (α, β)-derivations

On commutativity of 3-prime near-rings with generalized (α, β)-derivations

On Lie ideals with left derivationsin 3-prime near-rings

On Lie ideals with left derivationsin 3-prime near-rings

Commutativity in 3-prime nearrings through permutation identities

In this paper, we investigate permutation identities satisfied by semigroup left ideals and weak semigroup left ideals in prime nearrings. We obtain results on commutativity of multiplication and addition using these identities. We provide examples to show the necessity of certain conditions in some of the results obtained. Finally, we give a characterization of Galois field in terms of permutation identities.

Homoderivations and semigroup ideals in $3$-prime near-rings

This paper studies homoderivations satisfying certain conditions on semigroup ideals of near-rings. In addition, we include some examples of the necessity of the hypotheses used in our results.

Some Identities of 3-Prime Near-Rings Involving Jordan Ideals and Left Generalized Derivations

In the current paper, we study the structure of Jordan ideals of a 3-prime near-ring which satisfies some algebraic identities involving left generalized derivations and right centralizers. The limitations imposed in the hypothesis were justified by examples.

Some Identities in Rings and Near-Rings with Derivations

In the present paper we investigate commutativity in prime rings and 3-prime near-rings admitting a generalized derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings and 3-prime near-rings have been generalized.