The extension dimension of group graded rings

Abstract

In this paper, we introduce the concept of graded extension dimension for a group graded ring R, denoted by gr.ext.dim(R). We prove that when R is strongly graded, its graded extension dimension coincides with the non-graded extension dimension of both R itself and its degree-zero subring Re. Furthermore, we demonstrate that graded equivalence and graded separable equivalence preserve the extension dimension under appropriate conditions.

Theorems 3.3 and 3.12 in this paper contain fundamental errors that invalidate the main results.Theorem 3.3 falsely equates the extension dimension of a strongly graded ring with that of its degree-zero component.Theorem 3.12 relies on Theorem 3.3.The authors therefore withdraw this paper