Cohen-Macaulay and Gorenstein finitely graded rings (Q1109086)

The main purpose of this paper is to characterize Cohen-Macaulay and Gorenstein graded rings of finite support (i.e. with only finitely many nonzero homogeneous components). One of the consequences of these characterizations is the following: If R is a strongly graded commutative ring over a finite group G, and e is the unit element of G, then R is Cohen-Macaulay (resp. Gorenstein) if and only if \(R_ e\) is so. The results are applied to the case of semitrivial extensions.