Feckly reduced rings


ÜNGÖR B., Gurgun O., HALICIOĞLU S., Harmanci A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.44, no.2, pp.375-384, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.15672/hjms.2015449413
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.375-384

Abstract

Let R be a ring with identity and J(R) denote the Jacobson radical of R. In this paper, we introduce a new class of rings called feckly reduced rings. The ring R is called feckly reduced if R/J(R) is a reduced ring. We investigate relations between feckly reduced rings and other classes of rings. We obtain some characterizations of being a feckly reduced ring. It is proved that a ring R is feckly reduced if and only if every cyclic projective R-module has a feckly reduced endomorphism ring. Among others we show that every left Artinian ring is feckly reduced if and only if it is 2-primal, R is feckly reduced if and only if T(R, R) is feckly reduced if and only if R[x]/ < x(2) > is feckly reduced.