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2010•Journal of Anhui Normal UniversityRequires access

Some Studies on Strongly Regular Rings

Jun Wu

Open publisher page 7 citations

Abstract

In this paper,we mainly proved that the following conditions are equivalent:(1) R is a strongly regular ring;(2) R is a ELT-semi-prime ring,and for every essential left ideal L of R,(R/L)R is flat,every maximal left ideal or maximal right ideal of R is GW-ideal;(3) R is a ZC-ring,every maximal essential left ideal of R is GW-ideal and every simple singular left R-module is either GP-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 ring;(2) R is a ELT-semi-prime ring,and for every essential left ideal L of R,(R/L)R is flat,every maximal left ideal or maximal right ideal of R is GW-ideal;(3) R is a ZC-ring,every maximal essential left ideal of R is GW-ideal and every simple singular left R-module is either GP-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 ring;(2) R is a ELT-semi-prime ring,and for every essential left ideal L of R,(R/L)R is flat,every maximal left ideal or maximal right ideal of R is GW-ideal;(3) R is a ZC-ring,every maximal essential left ideal of R is GW-ideal and every simple singular left R-module is either GP-injective or flat.

Key concepts: Ideal (ethics), Maximal ideal, Mathematics, Minimal ideal, Prime (order theory), Ring (chemistry), Prime ideal, Regular ring

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