Results 31 to 40 of about 128 (117)

Unit-Regularity of Regular Nilpotent Elements [PDF]

Algebras and Representation Theory, 2016
Let $a$ be a regular element of a ring $R$. If either $K:=\rm{r}_R(a)$ has the exchange property or every power of $a$ is regular, then we prove that for every positive integer $n$ there exist decompositions $$ R_R = K \oplus X_n \oplus Y_n = E_n \oplus X_n \oplus aY_n,$$ where $Y_n \subseteq a^nR$ and $E_n \cong R/aR$.
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The Nilpotent Regular Element Problem [PDF]

Canadian Mathematical Bulletin, 2016
AbstractWe use George Bergman’s recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element x need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent
Pere Ara, Kevin C. O’Meara
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Regular Nilpotent Elements and Quantum Groups [PDF]

Communications in Mathematical Physics, 1999
23 pages, LaTeX ...
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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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m-rnc rings [PDF]

BIO Web of Conferences
In this article, an element w of an associative ring R is called m-regular nil clean or m-rnc if expressed as w = am + b where am is m-regular element and b is a nilpotent element. R is named m-regular nil clean ring or m-rnc ring. If all the elements of
Mahmood Ali Sh., Mohammed Ibraheem Zubaida   +1 more
doaj   +1 more source

Lipschitz groups and Lipschitz maps [PDF]

International Journal of Group Theory, 2017
‎‎This contribution mainly focuses on some aspects of Lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with Lipschitz multiplication and inversion map‎. ‎In the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be ...
Laurent Poinsot
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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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The Natural Components of a Regular Linear System

Oxford Bulletin of Economics and Statistics, EarlyView.
ABSTRACT The analysis of a finite‐dimensional regular linear system may be simplified by separating the system into its natural components. The natural components are smaller linear systems on separate subspaces whose dimensions sum to the dimension of the original linear system.
Brendan K. Beare, Phil Howlett
wiley   +1 more source

A Remark on Quadrics in Projective Klingenberg Spaces over a Certain Local Algebra

Mathematics, 2020
This article is devoted to some polar properties of quadrics in the projective Klingenberg spaces over a local ring which is a linear algebra generated by one nilpotent element.
Marek Jukl
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A classification of Prüfer domains of integer‐valued polynomials on algebras

Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.
Abstract Let D$D$ be an integrally closed domain with quotient field K$K$ and A$A$ a torsion‐free D$D$‐algebra that is finitely generated as a D$D$‐module and such that A∩K=D$A\cap K=D$. We give a complete classification of those D$D$ and A$A$ for which the ring IntK(A)={f∈K[X]∣f(A)⊆A}$\textnormal {Int}_K(A)=\lbrace f\in K[X] \mid f(A)\subseteq A ...
Giulio Peruginelli, Nicholas J. Werner
wiley   +1 more source