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An embedding theorem for weakly regular and fully idempotent rings

An embedding theorem for weakly regular and fully idempotent rings
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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
Adel Abyzov
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Weakly and Strongly Regular Near-rings

Algebra Colloquium, 2005
In this paper, we prove some basic properties of left weakly regular near-rings. We give an affirmative answer to the question whether a left weakly regular near-ring with left unity and satisfying the IFP is also right weakly regular. In the last section, we use among others left 0-prime and left completely prime ideals to characterize strongly ...
Groenewald, NJ, Argac, N
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Weakly Regular Rings

Canadian Mathematical Bulletin, 1973
This paper attempts to generalize a property of regular rings, namely,I2=Ifor every right (left) ideal. Rings with this property are called right (left) weakly regular. A ring which is both left and right weakly regular is called weakly regular. Kovacs in [6] proved that, for commutative rings, weak regularity and regularity are equivalent conditions ...
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Semiregular, weakly regular, and π-regular rings

Journal of Mathematical Sciences, 2002
This is a survey paper related to regular rings and their generalizations. It introduces many rings and modules, such as: semiregular and regular modules, semiregular and regular rings, semiprime and nonsingular rings, weakly \(\pi\)-regular and weakly regular rings, strongly \(\pi\)-regular and \(\pi\)-regular rings, rings of quotients and Pierce ...
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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
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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).
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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
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Weakly regular rings

Communications in Algebra, 1994
Victor Camillo, Yufei Xiao
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ON WEAKLY REGULAR RINGS AND GENERALIZATIONS OF V-RINGS

2011
In this paper, we have studied weakly regular rings and some generalizations of V-rings via GW-ideals. We have shown that: (1) If R is a left weakly regular ring whose maximal left (right) ideals are GW-ideals, then R is strongly regular; (2) If R is a right weakly regular ring whose maximal essential left ideals are GW-ideals, then R is ELT regular ...
Subedi, Tikaram, Buhphang, A. M.
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