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2012•Journal of Algebra and Its ApplicationsRequires access

WHEN CF RINGS ARE ARTINIAN

Wenxi Li, Jianlong Chen

Open publisher page 6 citations

Abstract

Let R be a ring, R is called a right ACS ring if the right annihilator of each element is essential in a direct summand of R. We prove that right CF ring is right artinian under right ACS condition. In particular, FGF conjecture is true under right ACS condition. We also give some conditions under which right noetherian left P-injective and left ACS ring is QF.

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What this paper is about

Let R be a ring, R is called a right ACS ring if the right annihilator of each element is essential in a direct summand of R. We prove that right CF ring is right artinian under right ACS condition. In particular, FGF conjecture is true under right ACS condition. We also give some conditions under which right noetherian left P-injective and left ACS ring is QF.

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Available abstract

Let R be a ring, R is called a right ACS ring if the right annihilator of each element is essential in a direct summand of R. We prove that right CF ring is right artinian under right ACS condition. In particular, FGF conjecture is true under right ACS condition. We also give some conditions under which right noetherian left P-injective and left ACS ring is QF.

Key concepts: Mathematics, Artinian ring, Annihilator, Radical of a ring, Primitive ring, Semisimple module, Noetherian, Ring (chemistry)

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