Results 191 to 200 of about 4,289,373 (226)

Reduced Near-Rings

1987
Abstract In this paper we introduce a partial order relation in a reduced near-ring and show that the set of all idempotents of a reduced near-ring with identity forms a Boolean algebra under this partial ordering. Further we introduce the notions hyper atom and orthogonal subsets in a reduced near-ring with identity and show that a reduced near-ring
D. Ramakotaiah, V. Sambasivarao
openaire   +1 more source

Actions of Lie Superalgebras on Reduced Rings

Algebras and Representation Theory, 2007
The authors consider actions of finite-dimensional Hopf algebras on reduced and graded-reduced algebras and study the question of when the subalgebra of invariants is non-zero. The first result says that if \(R\) is a graded-reduced ring of characteristic \(p>2\) acted on by a finitely generated restricted \(K\)-Lie superalgebra \(L\), where \(K\) is a
Bergen, Jeffrey, Grzeszczuk, Piotr, Hryniewicka, Małgorzata   +2 more
openaire   +1 more source

A note on connected reduced rings

Journal of Commutative Algebra, 2021
This short note illustrates a constructive proof of a characterisation of reduced and connected rings, whereas the cassical proof makes an apparently fundamental use of prime ideals and Krull's Lemma. Avoiding these constructively non-admissible tools has been achieved by using instead radical ideals and their properties, which are constructively ...
openaire   +2 more sources

Modules With Reduced Endomorphism Rings

Journal of Algebra and Its Applications
In this paper, we study endo-reduced modules as modules whose endomorphism rings have no nonzero nilpotent elements. We characterize their properties for different classes of modules, including [Formula: see text]-non-singular modules, multiplication modules and finitely generated modules over commutative Dedekind domains.
David Ssevviiri, Philly Ivan Kimuli
exaly   +2 more sources

A Simple Proof of a Theorem on Reduced Rings

Canadian Mathematical Bulletin, 1980
We give a simple proof of a theorem by Andrunakievič and Rjabuhin which states that a reduced ring is a subdirect product of entire rings. Our proof makes no use of m-systems and is in some sense similar to the proof of the corresponding theorem in the commutative case due to Krull.A reduced ring is a ring without non-zero nilpotent elements.
openaire   +1 more source

NPP RINGS, REDUCED RINGS AND SNF RINGS

2008
A ring R is called left NP P if for any nilpotent element a of R, l(a) = Re, e2 = e ∈ R. A right R−module M is called N f lat if for each a ∈ N(R), the Z−module map 1M ⊗ i : M ⊗R Ra −→ M ⊗R R is monic, where i : Ra ,→ R is the inclusion map. A ring R is called right SNF if every simple right R−module is N f lat. In this paper, we first show that a ring
WEİ, Junchao, CHEN, Jianhua
openaire   +1 more source

Rings decomposed into direct sums of nil rings and certain reduced rings

Mathematical Journal of Okayama University, 1985
Let R be a ring, E the set of idempotents of R, and N the set of nilpotents. For \(x\in R\), denote by r(x) the right annihilator of x; call x a right p.p. element if there exists \(e\in E\) such that \(xe=x\) and \(r(x)=r(e)\). Let P be the set of all right p.p. elements, and call R a generalized right p.p.
Hirano, Yasuyuki, Tominaga, Hisao
openaire   +3 more sources

ON REDUCED MODULES AND RINGS

2008
In this paper we extend several results known for reduced rings to reduced modules. We prove that for a semiprime module or a module with zero Jacobson radical, the concepts of reduced, symmetric, ps-Armendariz and ZI modules coincide. New examples of reduced modules are furnished: flat modules over reduced rings and modules with zero Jacobson radical ...
REGE, Mangesh B., BUHPHANG, A. M.
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Reduced morphisms and Nagata rings

Archiv der Mathematik, 1993
The paper is mainly devoted to a generalization of a criterion for Nagata rings given previously by \textit{K. Langmann} [Arch. Math. 55, No. 2, 139- 142 (1990; Zbl 0675.13007)]. The present generalization includes, among others, the case of arbitrary characteristic which was not covered by the paper cited above.
openaire   +1 more source

The Reduced Ring Order and Lower Semi-Lattices II

Journal of Algebra and Its Applications, 2021
Robert Raphael
exaly