Results 21 to 30 of about 16,976 (247)

The generating hypothesis in the derived category of a ring [PDF]

, 2006
We show that a strong form (the fully faithful version) of the generating hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von Neumann regular. This extends results of the second author.
Hovey, Mark, Lockridge, Keir, Puninski, Gena   +2 more
core   +1 more source

Classification of Boolean algebras through von Neumann regular $\mathcal{C}^{\infty}-$rings [PDF]

Categories and General Algebraic Structures with Applications
In this paper, we introduce the concept of a ``von Neumann regular $\mathcal{C}^{\infty}$-ring", which is a model for a specific equational theory.
Jean Berni, Hugo Mariano
doaj   +1 more source

A-D3 Modules and A-D4 Modules

Journal of Mathematics, 2023
Let A be a class of some right R-modules that is closed under isomorphisms, and let M be a right R-module. Then M is called A-D3 if, whenever N and K are direct summands of M with M=N+K and M/K∈A, then N∩K is also a direct summand of M; M is called an A ...
Zhanmin Zhu
doaj   +1 more source

On n-flat modules and n-Von Neumann regular rings

International Journal of Mathematics and Mathematical Sciences, 2006
We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n−1)-ring (resp., a weakly (n,n−1)-ring). We also give a new characterization of n-Von Neumann regular rings and a characterization of weak n-Von Neumann regular rings ...
Najib Mahdou
doaj   +1 more source

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

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, Hartwig RE, Pedro Patrício   +2 more
core   +1 more source

Relative Regular Modules. Applications to von Neumann Regular Rings [PDF]

Applied Categorical Structures, 2009
6 ...
openaire   +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

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