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2012•Journal of Anhui Normal UniversityRequires access

The Strong Regularity of Rings Whose Maximal Essential One-Sided Ideals are GW-Ideals

Jun Wu

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Abstract

In this paper,we mainly proved that the following conditions are equivalent:(1) R is a strongly regular rins;(2) R is a J-left weakly regular ring,and every maximal essential left ideal of R is GW-ideal;(3) R is a CN-ring,every maximal essential left ideal of R is GW-ideal,and every simple singular left R-module is either YJ-injective or flat.

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What this paper is about

In this paper,we mainly proved that the following conditions are equivalent:(1) R is a strongly regular rins;(2) R is a J-left weakly regular ring,and every maximal essential left ideal of R is GW-ideal;(3) R is a CN-ring,every maximal essential left ideal of R is GW-ideal,and every simple singular left R-module is either YJ-injective or flat.

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Available abstract

In this paper,we mainly proved that the following conditions are equivalent:(1) R is a strongly regular rins;(2) R is a J-left weakly regular ring,and every maximal essential left ideal of R is GW-ideal;(3) R is a CN-ring,every maximal essential left ideal of R is GW-ideal,and every simple singular left R-module is either YJ-injective or flat.

Key concepts: Maximal ideal, Ideal (ethics), Mathematics, Minimal ideal, Ring (chemistry), Injective function, Regular ring, Pure mathematics

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