Abstract: In this paper we study some properties of GC-projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC-projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.
Abstract: We present linear codes over finite commutative rings
which are not necessarily Frobenius. We treat the notion of syndrome
decoding by using Pontrjagin duality. We also give a version of Delsarte-s
theorem over rings relating trace codes and subring subcodes.
Abstract: Let R be a ring and n a fixed positive integer, we
investigate the properties of n-strongly Gorenstein projective, injective
and flat modules. Using the homological theory , we prove that
the tensor product of an n-strongly Gorenstein projective (flat) right
R -module and projective (flat) left R-module is also n-strongly
Gorenstein projective (flat). Let R be a coherent ring ,we prove that
the character module of an n -strongly Gorenstein flat left R -module
is an n-strongly Gorenstein injective right R -module . At last, let
R be a commutative ring and S a multiplicatively closed set of R ,
we establish the relation between n -strongly Gorenstein projective
(injective , flat ) R -modules and n-strongly Gorenstein projective
(injective , flat ) S−1R-modules. All conclusions in this paper is
helpful for the research of Gorenstein dimensions in future.