GORENSTEIN FLAT-COTORSION MODULES OVER STRONGLY GROUP-GRADED ALGEBRAS

Suppose G is a group, k is a commutative ring, and R is a strongly G-graded k-algebra. Moore’s conjecture says that if H is a finite-index subgroup of G, then under a certain condition on G and H, a left R-module that is projective over RH is also projective over R. The main theme of this article is to study the behavior of Gorenstein flat-cotorsion modules over strongly graded algebras and especially to prove the validity of Moore’s conjecture for this class of modules.