On symmetric and skew-symmetric projective R-modules

Abstract EN

If R is a commutative ring with identity, a finitely generated R- module P is defined to be symmetric (skew- symmetric) projective (s.p) (s.s.p) R- module if and only if there exists a finite set ( a1, a2, an) of generators of P and an nxn symmetric (skew- symmetric) matrix M=[rij] with entries in R satisfies the following: 1) U (Mt) = U 1*) U (-M = U 2) Uꓕ = ann(Mt) 2*) U1 = - ann(Mt) In this paper, two kinds of projective modules are considered, we prove that, the homomorphic image and the product of two (s.p) R- modules is (s.p) R- modules, some relations between (s.p) and (s.s.p) R- modules are proved.

The dual module P* and the bidual module P* of (s.p) and (s.s.p) R- module are studied.