Feckly reduced rings

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.

Keywords

• reduced ring,feckly reduced ring

References

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