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If we were very clever, we might be able to solve the following problem: Let A be a noetherian N-graded connected k-algebra given by generators and relations. Now determine, by looking at the relations, if A is AS-Gorenstein.

It must, however, be admitted that the problem as stated seems rather hard. A more modest goal is hence the following: Find some criteria by which it can be decided whether some naturally occurring algebras are AS-Gorenstein. That is what we shall do in this paper. We prove generalizations of several well-known theorems from commutative algebra, notably Watanabe's theorem [2, Theorem5. 3.2] and Stanley's theorem [10, Theorem4. 4]. Throughout this paper,``algebra''means connected N-graded algebra over a base field k. The main results are the following: