COTORSION DIMENSIONS OVER GROUP RINGS

Document Type : Original Manuscript

Author

Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandarabbas, Iran.

Abstract

Let

Γ

be a group,

Γ^{'}

a subgroup of

Γ

with finite index and

M

be a

Γ

-module. We show that

M

is cotorsion if and only if it is cotorsion as a

Γ^{'}

-module. Using this result, we prove that the global cotorsion dimensions of rings

Z Γ

and

Z Γ^{'}

are equal.

Keywords