$\ddot{I}‰$-left approximation dimensions under Stable equivalence

Abstract

In this paper, we investigate some transfer properties of $\ddot{I}‰$-left approximation dimensions of modules of stably equivalent Artin algebras having neither nodes nor semisimple direct summands. As applications, we give a one-to-one correspondence between basic (Wakamatsu) tilting modules, and prove that the Wakamatsu tilting conjecture is preserved under those equivalences.

17 pages