Results 231 to 240 of about 107,019 (266)
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The regularity of munn rings and semigroup rings
Acta Mathematica Sinica, 1995A ring means an associative ring, modules over rings are left ones. A ring \(R\) is said to have the strong IBN property iff every free \(R\)- module of any rank \(n\) cannot be generated by less than \(n\) elements. Let \(M_n (R)\) denote the full matrix ring of degree \(n\) over \(R\).
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On regular rings and continuous rings, III
Annali di Matematica Pura ed Applicata, 1984[Part II, cf. Kyungpook Math. J. 21, 171-176 (1981; Zbl 0516.16007).] A left A-module M is called FK-injective if, for any left submodule F isomorphic to a complement nonzero left submodule K of M, any relative complement C of \({}_ AF\) in \({}_ AM\) and any left submodule L of M containing \(C+F\), every epimorphism of \({}_ AL\) into \({}_ AK ...
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Mathematische Zeitschrift, 1971 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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Russian Mathematics, 2011
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Monatshefte f�r Mathematik, 1979
In this note, certain generalisations of strongly regular rings are considered in connection with regular rings andV-rings. The result that strongly regular rings are left (and right)V-rings [11] is extended. A condition for prime leftV-rings to be primitive with non-zero socle is given (this is related to a question ofFisher [7, Problem 3].
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In this note, certain generalisations of strongly regular rings are considered in connection with regular rings andV-rings. The result that strongly regular rings are left (and right)V-rings [11] is extended. A condition for prime leftV-rings to be primitive with non-zero socle is given (this is related to a question ofFisher [7, Problem 3].
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The complete matrix ring over an adjoint regular ring is adjoint regular
Semigroup Forum, 2009A ring \(R\) is adjoint regular if \(R\) forms a regular semigroup with respect to the circle composition \(a\circ b=a+b-ab\). \textit{X.-K. Du} [Northeast. Math. J. 4, No. 4, 463-468 (1988; Zbl 0697.16007)] has conjectured that the ring \(R_n\) of all \(n\times n\) matrices over \(R\) is adjoint regular whenever \(R\) is.
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Proceedings of the American Mathematical Society, 1973
Armendariz, E. P., Fisher, Joe W.
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Armendariz, E. P., Fisher, Joe W.
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Regular and generalized regular rings
1974During his study of continuous geometries, J. von Neumann found that any complemented modular lattice satisfying certain mild conditions arises from a specific type of ring, which he termed a regular ring. In the first place, these rings turn out to be a generalization of artinian semisimple rings, and subsequent studies have shown that the concepts of
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Cancellation of Projective Modules Over Regular Rings With Comparability
Journal of Pure and Applied Algebra, 1996Pere Ara, K C O'Meara
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