Results 11 to 20 of about 110,346 (305)

Regular rings and integral extension of a regular ring [PDF]

Proceedings of the American Mathematical Society, 1972
In this paper we show that a ring (not necessarily commutative) with identity element and without nonzero nilpotent elements is a von Neumann regular ring if every completely prime ideal is a maximal right ideal. Using this result, we show an integral extension (not necessarily commutative) without nonzero nilpotent elements of a regular ring is itself
Edward T. Wong
openaire   +4 more sources

On Generalized Regular Local Ring [PDF]

Science Journal of University of Zakho, 2015
A ring R is called a generalized Von Neumann regular local ring (GVNL-ring) if for any a∈R, either a or (1-a) is π-regular element. In this paper, we give some characterization and properties of generalized regular local rings.
Zubayda M. Ibraheem, Naeema A. Shereef
doaj   +2 more sources

Unit-regularity and representability for semiartinian $*$-regular rings [PDF]

Archivum Mathematicum, 2020
We show that any semiartinian subdirectly irreducible *-regular ring R admits a representation within some inner product space.
Herrmann, Christian
openaire   +5 more sources

The Regular Graph of a Non-Commutative Ring [PDF]

Electronic Notes in Discrete Mathematics, 2013
AbstractLet $R$ be a ring and $Z(R)$ be the set of all zero-divisors of $R$. The total graph of $R$, denoted by $T(\Gamma (R))$ is a graph with all elements of $R$ as vertices, and two distinct vertices $x, y\in R$ are adjacent if and only if $x+ y\in Z(R)$. Let the regular graph of $R$, $\mathrm{Reg} (\Gamma (R))$, be the induced subgraph of $T(\Gamma
Saieed Akbari, Farideh Heydari
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Some Results on W-regular Rings [PDF]

NTU Journal of Pure Sciences
Von Neumann regular rings, introduced in 1936, form a cornerstone of abstract algebra and were later extended to weakly regular rings. This work considers another extension, the W-regular rings defined by Wei [6], and explores their properties and ...
Hazim Tallat Hazim
doaj   +3 more sources

-Regular Modules [PDF]

Journal of Applied Mathematics, 2013
We introduced and studied -regular modules as a generalization of -regular rings to modules as well as regular modules (in the sense of Fieldhouse). An -module is called -regular if for each and , there exist and a positive integer such that .
Areej M. Abduldaim, Sheng Chen
doaj   +2 more sources

Smarandache rings [PDF]

, 2002
Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and ...
Vasantha, Kandasamy
core   +1 more source

Imbedding a Regular Ring in a Regular Ring with Identity [PDF]

Nagoya Mathematical Journal, 1966
In [1] L. Fuchs and I. Halperin have proved that a regular ring R is isomorphic to a two-sided ideal of a regular ring with identity. ([1] Theorem 1). Their methed is to imbed the regular ring R in the ring of all pairs (a, p) with a ∊ R and p from a suitable commutative regular ring S with identity such that R is an algebra over S.
openaire   +2 more sources

Varieties of ∗-regular rings [PDF]

Mathematica Slovaca, 2020
Abstract Given a subdirectly irreducible ∗-regular ring R, we show that R is a homomorphic image of a regular ∗-subring of an ultraproduct of the (simple) eRe, e in the minimal ideal of R; moreover, R (with unit) is directly finite if all eRe are unit-regular.
openaire   +2 more sources

SMARANDACHE SPECIAL DEFINITE ALGEBRAIC STRUCTURES [PDF]

, 2009
Introducing the notion of Smarandache special definite algebraic structures, also called equivalently as Smarandache definite special algebraic structures.
Vasantha, Kandasamy
core   +1 more source