Results 201 to 210 of about 82,151 (248)

Right Weakly Regular Rings: A Survey

, 2010
A ring is right weakly regular (r.w.r.) if every right ideal of the ring is idempotent. Such rings are also called fully right idempotent. This paper gives a survey of the theory of r.w.r. rings and some closely allied topics, from its origins in the early 1950’s up to the present state-of-the-art. The paper contains sections on: equivalent conditions,
Henry E. Heatherly, Ralph P. Tucci
semanticscholar   +3 more sources

Weakly regular modules over normal rings

Siberian Mathematical Journal, 2008
Summary: Under study are some conditions for the weakly regular modules to be closed under direct sums and the rings over which all modules are weakly regular. For an arbitrary right \(R\)-module \(M\), we prove that every module in the category \(\sigma(M)\) is weakly regular if and only if each module in \(\sigma(M)\) is either semisimple or contains
А. N. Abyzov
openaire   +5 more sources

Semiregular and Weakly Regular Rings

, 2002
For a module M, we say that a submodule N of M lies above a direct summand of M if there is a direct decomposition M = P⊕Q such that P⊆N and Q⋂N is a superfluous submodule of Q. In this case, Q⋂N is a superfluous submodule of M and Q⋂N⊆J(M).
A. A. Tuganbaev
openaire   +2 more sources

On weakly regular modules over commutative rings

Journal of Algebra and Its Applications
In this paper, we introduce the class of weakly (von Neumann) regular modules and study its algebraic properties. We present some characterization of this class of modules. Finally, we show that a ring [Formula: see text] is perfect if and only if every [Formula: see text]-module is weakly regular.
Dawood Hassanzadeh-Lelekaami, Hajar Roshan-Shekalgourabi   +1 more
openaire   +2 more sources

Weakly regular rings

Communications in Algebra, 1994
Victor Camillo, Yufei Xiao
openaire   +2 more sources

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Central extensions of associative algebras and weakly action representable categories

Theory and Applications of Categories, 2022
A central extension is a regular epimorphism in a Barr exact category $\mathscr{C}$ satisfying suitable conditions involving a given Birkhoff subcategory of $\mathscr{C}$ (joint work with G. M. Kelly, 1994).
G. Janelidze
semanticscholar   +1 more source

Rings Whose Non-Invertible Elements are Strongly Weakly Nil-Clean

Journal of Algebra and its Applications
The target of the present work is to give a new insight in the theory of strongly weakly nil-clean rings, recently defined by Kosan and Zhou in the Front. Math. China (2016) and further explored in detail by Chen-Sheibani in the J. Algebra Appl.
P. Danchev, Mina Doostalizadeh, O. Hasanzadeh, A. Javan, A. Moussavi   +4 more
semanticscholar   +1 more source

Module-theoretic generalization of commutative von Neumann regular rings

Communications in Algebra, 2019
Jayaram and Tekir defined an R-module M, R is a commutative ring, to be “von Neumann regular” if for each there exists an such that Previously, Fieldhouse called M “regular” if every submodule is pure and Ramamurthi and Rangaswamy called M “strongly ...
D. D. Anderson, S. Chun, J. R. Juett
semanticscholar   +1 more source

Coloring of cozero-divisor graphs of commutative von Neumann regular rings

Proceedings - Mathematical Sciences, 2018
Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R , denoted by $$\Gamma ^{\prime }(R)$$ Γ ′ ( R ) , is a graph with vertices in $$W^*(R)$$ W ∗ ( R ) , which is the set of all non-zero and non-unit elements of R , and two ...
M. Bakhtyiari, R. Nikandish, M. Nikmehr
semanticscholar   +1 more source

Some notes on weakly *-reversible rings

International Journal of Algebra, 2019
A ring R is called weakly ∗−reversible if ab = 0 implies that Rb∗ra is a nil left ideal of R for all a, b, r ∈ R. In this paper, we continue the study of weakly ∗−reversible ring.
W. Fakieh
semanticscholar   +1 more source