Feckly reduced rings

Year 2015, Volume: 44 Issue: 2, 375 - 384, 01.04.2015

Burcu Ungor , Orhan Gurgun Sait Halicioglu , Abdullah Harmanci

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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