Abstract
Let R be a commutative Noetherian local Gorenstein ring with residue field k. We show that G(k), the Gorenstein injective envelope of k, is an artinian R-module, and we compute G(k) in the case where R = k[[S]] is a semigroup ring and S is symmetric. We also show that a certain subring of the endomorphism ring of G(k) is a complete local (but possibly non-commutative) ring.
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