Results 31 to 40 of about 375 (165)

Strongly 2T - Clean Rings [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics
An element a in a ring R is referred to be strongly 2T-clean (2 – STC element for short), a = Ω-Λ+u, where Ω,Λ are idempotent elements and u is a unit elements of order three.
Zeina Hamady, Nazar Shuker
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Nilpotent elements and Armendariz rings

Journal of Algebra, 2008
Let \(R\) denote an associative ring with \(1\), and let \(\text{nil}(R)\) denote the set of nilpotent elements. Further, let \(f(x)=\sum_{i=0}^ma_ix^i,g(x)=\sum_{j=0}^nb_jx^j\in R[x]\) denote two arbitrary polynomials. One says that \(R\) is an Armendariz ring if \(f(x)g(x)=0\) implies that \(a_ib_j=0\) for all \(i\) and \(j\).
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Infinite-Dimensional Modular Lie Superalgebra Ω

Abstract and Applied Analysis, 2013
All ad-nilpotent elements of the infinite-dimensional Lie superalgebra Ω over a field of positive characteristic are determined. The natural filtration of the Lie superalgebra Ω is proved to be invariant under automorphisms by characterizing ad-nilpotent
Xiaoning Xu, Bing Mu
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On sub-class sizes of mutually permutable products

Open Mathematics, 2021
In this paper, we investigate the influence of sub-class sizes on a mutually permutable factorized group in which the sub-class sizes of some elements of its factors have certain quantitative properties. Some criteria for a group to be pp-nilpotent or pp-
Li Jinbao, Yang Yong
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Amalgamated rings with m-nil clean properties

Ratio Mathematica, 2023
In this paper, we study the transfer of the notion of $m$-nil clean (i.e., a ring in which  every element is a sum of a nilpotent and  an $m$-potent elements) to the amalgamarted rings.
Vijayanand Venkatachalam, Selvaraj Chelliah   +1 more
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Nilpotent Elements in Lie Algebras

Journal of Algebra, 1990
A classical result of \textit{Fine} and \textit{Herstein} is that the number of n by n nilpotent matrices with entries in GF(q) is a power of q, that power being \(n^ 2-n\). Kaplansky formulates an analogous problem in Lie algebras as follows: For a simple Lie algebra L of n by n matrices with entries from a field of q elements, is the number of ...
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Some Residual Properties of Finite Rank Groups

Моделирование и анализ информационных систем, 2014
The generalization of one classical Seksenbaev theorem for polycyclic groups is obtained. Seksenbaev proved that if G is a polycyclic group which is residually finite p-group for infinitely many primes p, it is nilpotent. Recall that a group G is said to
D. N. Azarov
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On the generalization of pseudo p-closure in pseudo BCI-algebras [PDF]

Journal of Hyperstructures
In this paper, the notion of generalization of pseudo p-closure, denoted by gcl, is introduced and its related properties are investigated. The gcl of subalgebras and pseudo-ideals is discussed.
Padena Pirzadeh Ahvazi, Habib Harizavi, Tayebeh Koochakpoor   +2 more
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On Weak-BCC-Algebras

The Scientific World Journal, 2013
We describe weak-BCC-algebras (also called BZ-algebras) in which the condition is satisfied only in the case when elements belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras.
Janus Thomys, Xiaohong Zhang
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A typical graph structure of a ring [PDF]

Transactions on Combinatorics, 2015
The zero-divisor graph of a commutative ring R with respect to nilpotent elements is a simple undirected graph $Gamma_N^*(R)$ with vertex set Z_N(R)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where Z_N(R)={x
R. Kala , S. Kavitha
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