Results 21 to 30 of about 16,962 (297)
A commutativity theorem for left s-unital rings
International Journal of Mathematics and Mathematical Sciences, 1990 In this paper we generalize some well-known commutativity theorems for associative rings as follows: Let R be a left s-unital ring. If there exist nonnegative integers m>1, k≥0, and n≥0 such that for any x, y in R, [xky−xnym,x]=0, then R is commutative.
Hamza A. S. Abujabal
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Cluster algebras of infinite rank [PDF]
, 2014 Holm and Jørgensen have shown the existence of a cluster structure on a certain category D that shares many properties with finite type A cluster categories and that can be fruitfully considered as an infinite analogue of these. In this work we determine
Gratz, Sira +3 more
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On The Roots of Unity in Several Complex Neutrosophic Rings
Neutrosophic Sets and Systems, 2023 Roots of unity play a basic role in the theory of algebraic extensions of fields and rings. The aim of this paper is to obtain an algorithm to find all n-th roots of unity in five different kinds of neutrosophic complex rings, where many theorems and examples will be illustrated and suggested.
Djamal Lhiani +3 more
openaire +2 more sources
Z-polynomials and ring commutativity [PDF]
, 2012 We characterise polynomials f with integer coefficients such that a ring with unity R is necessarily commutative if f(x) is central for all x Ɛ R.
Buckley, S.M. +2 more
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On commutativity of one-sided s-unital rings
International Journal of Mathematics and Mathematical Sciences, 1992 The following theorem is proved: Let r=r(y)>1, s, and t be non-negative integers. If R is a left s-unital ring satisfies the polynomial identity [xy−xsyrxt,x]=0 for every x,y∈R, then R is commutative. The commutativity of a right s-unital ring satisfying
H. A. S. Abujabal, M. A. Khan
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Nonessential sum graph of an Artinian ring [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”.
Bikash Barman, Kukil Kalpa Rajkhowa
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IDEMPOTENT ELEMENTS IN MATRIX RING OF ORDER 2 OVER POLYNOMIAL RING $\mathbb{Z}_{p^2q}[x]$ [PDF]
, 2023 An idempotent element in the algebraic structure of a ring is an element that, when multiplied by itself, yields an outcome that remains unchanged and identical to the original element. Any ring with a unity element generally has two idempotent elements,
Arifin, Muchammad Choerul, Ernanto, Iwan
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Commutativity theorems for rings with constraints on commutators
International Journal of Mathematics and Mathematical Sciences, 1991 In this paper, we generalize some well-known commutativity theorems for associative rings as follows: Let n>1, m, s, and t be fixed non-negative integers such that s≠m−1, or t≠n−1, and let R be a ring with unity 1 satisfying the polynomial identity ys[xn,
Hamza A. S. Abujabal
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CHARACTERIZATION OF JORDAN $\{g, h\}$-DERIVATIONS OVER MATRIX ALGEBRAS [PDF]
Journal of Algebraic Systems, 2023 In this article, we characterize $\{g, h\}$-derivation on the upper triangular matrix algebra $\mathcal{T}_n(C)$ and prove that every Jordan $\{g, h\}$-derivation over $\mathcal{T}_n(C)$ is a $\{g, h\}$-derivation under a certain condition, where $C$ is ...
Arindam Ghosh, Om Prakash
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The Coefficient Ring of a Primitive Group Ring [PDF]
, 1975 All rings are associative with unity. A ring R is prime if xRy ≠ 0 whenever x and y are nonzero. A ring R is (left) primitive if there exists a faithful irreducible left R-module.If the group ring R[G] is primitive, what can we say about R?
John Lawrence
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