A GENERALIZATION OF CORETRACTABLE MODULES

Document Type : Original Manuscript

Author

Department of Mathematics, University of Mazandaran, Babolsar, Iran

Abstract

Let

R

be a ring and

M

a right

R

-module. We call

M

,
coretractable relative to

\overset{―}{Z} (M)

(for short,

\overset{―}{Z} (M)

-coretractable)
provided that, for every proper submodule

N

M

containing

\overset{―}{Z} (M)

, there is
a nonzero homomorphism

f : \frac{M}{N} \to M

. We investigate some conditions
under which the two concepts coretractable and

\overset{―}{Z} (M)

-coretractable, coincide.
For a commutative semiperfect ring

R

, we show that

R

\overset{―}{Z} (R)

-coretractable
if and only if

R

is a Kasch ring. Some examples are provided to illustrate different concepts.

Keywords