Results 61 to 70 of about 2,745 (167)

The X-semiprimeness of rings

Journal of Algebra and Its Applications
For a nonempty subset [Formula: see text] of a ring [Formula: see text], the ring [Formula: see text] is called [Formula: see text]-semiprime if, given [Formula: see text], [Formula: see text] implies [Formula: see text]. This provides a proper class of semiprime rings. First, we clarify the relationship between idempotent semiprime and unit-semiprime
Grigore Călugăreanu, Tsiu-Kwen Lee, Jerzy Matczuk   +2 more
openaire   +2 more sources

A Note on Skew Derivations and Antiautomorphisms of Prime Rings

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this article, we investigate the behavior of a prime ring which admits a skew derivation satisfying certain functional identities involving an antiautomorphism. We employ tools such as generalized identities and commutativity‐preserving maps to analyze these rings.
Faez A. Alqarni, Nadeem U. R. Rehman, Hafedh Alnoghashi, Junaid Nisar, Omar Al-Mallah, Ali Jaballah   +5 more
wiley   +1 more source

A Study of Generalized Differential Identities via Prime Ideals

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Let R be a ring and P be a prime ideal of R. The aim of this research paper is to delve into the relationship between the structural properties of the quotient ring R/P and the behavior of generalized derivations in a ring R endowed with an involution.
Ali Yahya Hummdi, Kamal Charrabi, Shakir Ali, Abdellah Mamouni, Faranak Farshadifar   +4 more
wiley   +1 more source

Semiprime skew group rings

Journal of Algebra, 1978
In this paper we prove that if G is a finite group of automorphisms acting on a semiprime ring R such that R has no additive ] G j-torsion, then the skew group ring R*G is also semiprime. The result was heretofore known in such special cases as when G is finite abelian, R is Goldie, or R satisfies a polynomial identity [I]. Our technique of proof is to
Susan Montgomery, Joe W. Fisher
openaire   +2 more sources

Modules With Epimorphisms Between Their Submodules

Journal of Mathematics, Volume 2025, Issue 1, 2025.
An R‐module M is called weakly uniserial if its submodules are comparable regarding embedding, i.e., if for any two submodules N, K of M, HomR(N, K) or HomR(K, N) contains an injective element. Here, we are interested in studying modules which for any two submodules of them there is an epimorphism from one to the other.
P. Karimi Beiranvand, Pramita Mishra
wiley   +1 more source

Higher Derivations Satisfying Certain Identities in Rings

Journal of Mathematics, Volume 2024, Issue 1, 2024.
Let n and m be fixed positive integers. In this paper, we establish some structural properties of prime rings equipped with higher derivations. Motivated by the works of Herstein and Bell‐Daif, we characterize rings with higher derivations D=dii∈N satisfying (i) dnx,dmy∈ZR for all x,y∈R and (ii) dnx,y∈ZR for all x,y∈R.
Amal S. Alali, Shakir Ali, Naira N. Rafiquee, Vaishali Varshney, Faranak Farshadifar   +4 more
wiley   +1 more source

Pythagorean fuzzy nil radical of Pythagorean fuzzy ideal

Boletim da Sociedade Paranaense de Matemática
In this work, we introduce the Pythagorean fuzzy nil radical of a Pythagorean fuzzy ideal of a commutative ring, we further provide the notion of Pythagorean fuzzy semiprime ideal, and we study some related properties.
Idris Bachadach, A. Talhaoui, S. Melliani, Sofyane Achik   +3 more
doaj   +1 more source

On the notion of 'retractable modules' in the context of algebras [PDF]

, 2014
This is a survey on the usage of the module theoretic notion of a "retractable module" in the study of algebras with actions. We explain how classical results can be interpreted using module theory and end the paper with some open questions.Comment ...
Lomp, Christian
core   +1 more source

Stratification of prime spectrum of quantum solvable algebras

, 2001
A quantum solvable algebra is an iterated $q$-skew extension of a commutative algebra. We get finite statification of prime spectrum for quantum solvable algebras obeying some natural conditions.
Panov, A. N.
core   +2 more sources

Structure of Semiprime P.I. Rings [PDF]

Proceedings of the American Mathematical Society, 1973
In this paper we make an investigation into the structure of semiprime polynomial identity rings which is culminated by showing that each such ring R R has a unique maximal left quotient ring Q Q such that (1) Q Q is von Neumann regular with unity and (2) every regular element in R R
openaire   +1 more source