Results 11 to 20 of about 178 (166)

Affine polynomial identity rings and their generalizations

Journal of Algebra, 1979
Amiram Braun
exaly   +2 more sources

Group rings satisfying a polynomial identity

Journal of Algebra, 1972
D S Passman
exaly   +2 more sources

Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute

Open Mathematics, 2017
An element in a ring R with identity is said to be strongly nil clean if it is the sum of an idempotent and a nilpotent that commute, R is said to be strongly nil clean if every element of R is strongly nil clean. Let C(R) be the center of a ring R and g(
Handam Ali H., Khashan Hani A.
doaj   +1 more source

Subrings of I-rings and S-rings

International Journal of Mathematics and Mathematical Sciences, 1997
Let R be a non-commutative associative ring with unity 1≠0, a left R-module is said to satisfy property (I) (resp. (S)) if every injective (resp. surjective) endomorphism of M is an automorphism of M.
Mamadou Sanghare
doaj   +1 more source

Rings virtually satisfying a polynomial identity

Journal of Pure and Applied Algebra, 2005
Let \(f(x_1,\dots,x_n)\) be a nonzero polynomial without constant term in the free associative ring \(\mathbb{Z}\langle x_1,x_2,\dots\rangle\). A ring \(R\) is called an \(f\)-ring if it satisfies the polynomial identity \(f=0\); it is a virtual \(f\)-ring if for every \(n\) infinite subsets \(X_1,\dots,X_n\) of \(R\) there exist \(r_i\in X_i\) such ...
Abdollahi, Alireza, Akbari, Saieed
openaire   +1 more source

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
doaj   +1 more source

Eulerian Polynomial Identities on Matrix Rings

Journal of Algebra, 1993
It is well known that the Amitsur-Levitzki theorem can be proved using some graph-theoretical constructions, see, e.g. \textit{R. G. Swan} [Proc. Am. Math. Soc. 14, 367-373 (1963; Zbl 0118.018)]. The paper under review is a further development in this direction. Assume \(G\) is an Eulerian directed graph having \(k\) vertices and \(N\) edges, and let \(
Szigeti, Jenő, Tuza, Zsolt, Révész, Gábor   +2 more
openaire   +2 more sources

Group Rings Satisfying a Polynomial Identity. III [PDF]

Proceedings of the American Mathematical Society, 1971
Let K[G] denote the group ring of G over the field K and let A denote the F.C. subgroup of G. In this paper we show that if K[G] satisfies a polynomial identity of degree n, then [G: Al] < n/2. Moreover this bound is best possible. If K[G] satisfies a polynomial identity of degree n, then it is known that [G: A] < 0o.
openaire   +3 more sources

Hierarchical Identity-Based Signature in Polynomial Rings

The Computer Journal, 2020
Abstract Hierarchical identity-based signature (HIBS) plays a core role in a large community as it significantly reduces the workload of the root private key generator. To make HIBS still available and secure in post-quantum era, constructing lattice-based schemes is a promising option.
Zhichao Yang 0002, Dung Hoang Duong, Willy Susilo, Guomin Yang, Chao Li 0002, Rongmao Chen   +5 more
openaire   +2 more sources

S-J-Ideals: A Study in Commutative and Noncommutative Rings

Journal of Mathematics
In this paper, we introduce the concept of S-J-ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that many properties of J-ideals apply to S-J-ideals and examine their ...
Alaa Abouhalaka, Hatice Çay, Bayram Ali Ersoy   +2 more
doaj   +1 more source