Results 61 to 70 of about 2,898 (193)

On τ-centralizers of semiprime rings

Siberian Mathematical Journal, 2007
Summary: Let \(R\) be a semiprime 2-torsion free ring, and let \(\tau\) be an endomorphism of \(R\). Under some conditions we prove that a left Jordan \(\tau\)-centralizer of \(R\) is a left \(\tau\)-centralizer of \(R\). Under the same conditions we also prove that a Jordan \(\tau\)-centralizer of \(R\) is a \(\tau\)-centralizer of \(R\).
openaire   +4 more sources

Prime Graphs of Polynomials and Power Series Over Noncommutative Rings

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The prime graph PG(R) of a ring R is a graph whose vertex set consists of all elements of R. Two elements x, y ∈ R are adjacent in the graph if and only if xRy = 0 or yRx = 0. An element a ∈ R is called a strong zero divisor in R if 〈a〉〈b〉 = 0 or 〈b〉〈a〉 = 0 for some nonzero element b ∈ R. The set of all strong zero divisors is denoted by S(R).
Walaa Obaidallah Alqarafi, Wafaa Mohammed Fakieh, Alaa Abdullah Altassan, Shikha Binwal   +3 more
wiley   +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

Effects of Generalized Semiderivations on Algebraic Identities Involving Prime Ideals

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this article, instead of a generalized derivation, we will use the concept of a generalized semiderivation ∇ that satisfies various identities involving a prime ideal ß of an optional ring Λ to describe the behavior of a quotient ring Λ/ß. We will use this concept to generalize some well‐known results that studied the behavior of a ring Λ via a ...
Kholood Alnefaie, Pramita Mishra
wiley   +1 more source

On Prime and Semiprime Rings with Symmetric Generalized Biderivations

Al-Mustansiriyah Journal of Science, 2017
The propose of this paper is to present some results concerning the symmetric generalized Biderivations when their traces satisfies some certain conditions on an ideal of prime and semiprime rings.
Auday H. Mahmood, Dheaa K. Hussain K. Hussein   +1 more
doaj   +1 more source

Prime Ideal, Semiprime Ideal, and Radical of an Ideal of an L-Subring

Fuzzy Information and Engineering, 2023
In this paper, we develop a systematic theory for the ideals of an L-ring L(μ, R). We introduce the concepts of a prime ideal, a semiprime ideal, and the radical of an ideal in an L-ring. The notion of a maximal ideal has been introduced and discussed in
Anand Swaroop Prajapati, Naseem Ajmal, Iffat Jahan   +2 more
doaj   +1 more source

A Pair of Generalized (α, α)‐Derivations With Identities Related to Prime Ideals

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Let A be an arbitrary ring, α an automorphism of A, I a nonzero ideal of A, and ϒ a prime ideal of A satisfying the condition ϒ⊊αI. This research investigates the interplay between two generalized (α, α)‐derivations, Ω and G (associated with (α, α)‐derivations f and h, respectively), and the resulting characteristics of the quotient ring A/ϒ.
Ali Yahya Hummdi, Hafedh Alnoghashi, Radwan Mohammed Al-Omary, Abdelkarim Boua, Faranak Farshadifar   +4 more
wiley   +1 more source

A note on derivations in semiprime rings

International Journal of Mathematics and Mathematical Sciences, 2005
We prove in this note the following result. Let n>1 be an integer and let R be an n!-torsion-free semiprime ring with identity element. Suppose that there exists an additive mapping D:R→R such that D(xn)=∑j=1nxn−jD(x)xj−1 is fulfilled for all x∈R.
Joso Vukman, Irena Kosi-Ulbl
doaj   +1 more source

Coweakly Uniserial Modules and Rings Whose (2‐Generated) Modules Are Coweakly Uniserial

Journal of Mathematics, Volume 2025, Issue 1, 2025.
A module is called weakly uniserial if for any two its submodules at least one of them is embedded in the other. This is a nontrivial generalization of uniserial modules and rings. Here, we introduce and study the dual of this concept. In fact, an R‐module M is called coweakly uniserial if for any submodules N, K of M, HomR(M/N, M/K) or HomR(M/K, M/N ...
M. M. Oladghobad, R. Beyranvand, Faranak Farshadifar   +2 more
wiley   +1 more source

On a theorem of McCoy [PDF]

Mathematica Bohemica
We study McCoy's theorem to the skew Hurwitz series ring $({\rm HR}, \omega)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings.
Rajendra Kumar Sharma, Amit B. Singh
doaj   +1 more source