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2005•Chinese Annals of Mathematics,series ARequires access

SOME PROPERTIES OF ZERO COMMUTATIVE RINGS

Wenting Tong

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Abstract

This paper investigates some properties of zero commutative rings and extend some results from commutative rings to zero commutative rings. If R is a zero commutative ring, the authors obtain that (1) R is strongly regular if and only if every essential left ideal of R which is an annihilator is left GP-injective or R contains a maximal left ideal K such that the annihilator of every element of K is left GP-injective; (2) R is a GPP-ring if and only if it is a quasi π-regular ring and GPF-ring.

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What this paper is about

This paper investigates some properties of zero commutative rings and extend some results from commutative rings to zero commutative rings. If R is a zero commutative ring, the authors obtain that (1) R is strongly regular if and only if every essential left ideal of R which is an annihilator is left GP-injective or R contains a maximal left ideal K such that the annihilator of every element of K is left GP-injective; (2) R is a GPP-ring if and only if it is a quasi π-regular ring and GPF-ring.

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Available abstract

This paper investigates some properties of zero commutative rings and extend some results from commutative rings to zero commutative rings. If R is a zero commutative ring, the authors obtain that (1) R is strongly regular if and only if every essential left ideal of R which is an annihilator is left GP-injective or R contains a maximal left ideal K such that the annihilator of every element of K is left GP-injective; (2) R is a GPP-ring if and only if it is a quasi π-regular ring and GPF-ring.

Key concepts: Annihilator, Commutative ring, Mathematics, Primary ideal, Von Neumann regular ring, Zero (linguistics), Ring (chemistry), Injective function

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