GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE

Authors : M AMİNİ

Pages : 114-126

Doi:10.24330/ieja.662993

View : 13 | Download : 12

Publication Date : 2020-01-07

Article Type : Research Paper

Abstract :Let $T$ be a tilting module. In this paper, Gorenstein $\pi[T]$-projective modules are introduced and some of their basic properties are studied. Moreover, some characterizations of rings over which all modules are Gorenstein $\pi[T]$-projective are given. For instance, on the $T$-cocoherent rings, it is proved that the Gorenstein $\pi[T]$-projectivity of all $R$-modules is equivalent to the $\pi[T]$-projectivity of $\sigma[T]$-injective as a module.
Keywords : Cocoherent ring, dimension, Gorenstein module, tilting module