LIFTING MODULES WITH RESPECT TO A PRERADICAL

Document Type : Original Manuscript

Author

Department of Mathematics, Quchan University of Advanced Technologies, Quchan, Iran.

Abstract

Let

M

be a right module over a ring

R

t a u_{M}

a preradical on

s i g m a [M]

, and

N i n s i g m a [M]

. In this note we show that if

N_{1}, N_{2} i n s i g m a [M]

are two

t a u_{M}

-lifting modules such that

N_{i}

N_{j}

-projective (

i, j = 1, 2

), then

N = N_{1} o p l u s N_{2}

t a u_{M}

-lifting. We investigate when homomorphic image of a

t a u_{M}

-lifting module is

t a u_{M}

-lifting.

Keywords