Results 21 to 30 of about 16,929 (257)
The almost isomorphism relation for simple regular rings [PDF]
, 1992 A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K.C . O'Meara, and the authors.
Ara, Pere,, Goodearl, K. R.
core +2 more sources
Trivial Ring Extension of Suitable-Like Conditions and some properties [PDF]
مجلة جامعة النجاح للأبحاث العلوم الطبيعية, 2018 We investigate the transfer of the notion of suitable rings along with related concepts, such as potent and semipotent rings, in the general context of the trivial ring extension, then we put these results in use to enrich the literature with new ...
Khalid Adarbeh
doaj +1 more source
Relative Regular Modules. Applications to von Neumann Regular Rings [PDF]
Applied Categorical Structures, 2009 6 ...
openaire +2 more sources
ON φ-VON NEUMANN REGULAR RINGS [PDF]
Journal of the Korean Mathematical Society, 2013 Let R be a commutative ring with and let = {R|R is a commutative ring and Nil(R) is a divided prime ideal}. If , then R is called a -ring. In this paper, we introduce the concepts of -torsion modules, -flat modules, and -von Neumann regular rings.
Wei Zhao, Fanggui Wang, Gaohua Tang
openaire +1 more source
New characterizations of Von Neumann regular rings and a conjecture of Shamsuddin [PDF]
, 1996 A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a Von Neuman regular ring. We prove two theorems and
Faith, Carl
core +2 more sources
Injective and coherent endomorphism rings relative to some matrices
Open Mathematics, 2023 Let MM be a right RR-module with S=End(MR)S={\rm{End}}\left({M}_{R}). Given two cardinal numbers α\alpha and β\beta and a row-finite matrix A∈RFMβ×α(S)A\in {{\rm{RFM}}}_{\beta \times \alpha }\left(S), SM{}_{S}M is called injective relative to AA if ...
Zeng Yuedi
doaj +1 more source
Moore-Penrose invertibility in involutory rings: the case aa+=bb+ [PDF]
, 2010 In this article, we consider Moore-Penrose invertibility in rings with a general involution. Given two von Neumann regular elements a, b in a general ring with an arbitrary involution, we aim to give necessary and sufficient conditions to aa† = bb†. As a
C. Mendes Araújo +2 more
core +1 more source
A Generalized Primitive Element Theorem [PDF]
, 2007 We deal with the following variant of the primitive element theorem: any commutative strongly separable extension of a commutative ring can be embedded in another one having primitive element.
Bagio, Dirceu, Paques, Antonio
core +1 more source
K-Theoretically Simple Von Neumann Regular Rings
Journal of Algebra, 1995 The authors investigate the differences between simplicity of a von Neumann regular ring and simplicity of its ordered Grothendieck group \(K_0\). After giving preliminaries in \S 1, they derive properties of pseudo-rank functions on ideals in a regular ring. In \S 3 they prove that if \(R\) is a stably finite, \(K_0\)-simple, non-Artinian regular ring
Ara, P. +3 more
openaire +2 more sources
Self-injective von Neumann regular rings and Köthe's conjecture [PDF]
Journal of Pure and Applied Algebra, 2021 One of the many equivalent formulation of the K the's conjecture is the assertion that there exists no ring which contains two nil right ideals whose sum is not nil. We discuss several consequences of an observation that if the Koethe conjecture fails then there exists a counterexample in the form of a countable local subring of a suitable self ...
Kálnai, Peter, Žemlička, Jan
openaire +2 more sources