Weakly regular rings - Open Access .click

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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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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Weakly regular rings

Communications in Algebra, 1994
Victor Camillo
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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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mathematics
electronic computers. computer science
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reduced rings
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commutative algebra math.ac

weakly regular ring
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