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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 ...
N J Groenewald, N Argaç
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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 ...
V. S. Ramamurthi
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Weakly Regular Modules Over Normal Rings [PDF]
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
A N Abyzov
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Right Weakly Regular Rings: A Survey
2010A 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
2002For 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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Generalizing Unit-Regular Rings and Special Clean Elements
Proyecciones, 2020 As a strengthening of the definition of weakly clean rings, given by Šter in J. Algebra (2014), and as a common generalization of the classical unit-regular rings, we define and investigate the class of socalled weakly unit-regular rings as those rings R
Peter Danchev
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Semiregular, weakly regular, and π-regular rings
Journal of Mathematical Sciences, 2002This 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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On weakly regular modules over commutative rings
Journal of Algebra and Its ApplicationsIn 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 +1 more
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ON WEAKLY REGULAR RINGS AND GENERALIZATIONS OF V-RINGS
2011In 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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