Some results on the quotient of co-m modules

Document Type : Research Paper

Author

Department of Mathematics, University of Payame Noor,Tehran, Iran.

Abstract

Let

R

be a commutative ring with identity and let

M

be a
unitary

R

-module. In this paper, among various results, we prove that if

M

is a cancellation

R

-module and

L

is a nonzero simple submodule of

M

, then

L

is a copure submodule of

M

. Moreover, in this case, if

M

is co-m, then

M / L

is also a co-m

R

-module. We investigate various conditions under which the quotient module

M / N

of a co-m

M

is also a co-m. We prove that if

M

is a cancellation Noetherian co-m module, then for every second submodule

N

M

the quotient module

M / N

is a co-m

R

-module.
We obtain some results concerning socle and radical of co-m modules.

Keywords