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

Year 2020, Volume: 27 Issue: 27, 114 - 126, 07.01.2020

M. Amini

https://doi.org/10.24330/ieja.662993

Cited By: 2

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

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