The Gorenstein Injective Envelope of the Residue Field of a Local Ring
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.
gorenstein local ring, gorenstein injective, injective envelope
Belshoff, Richard G., and Edgar E. Enochs. "The Gorenstein injective envelope of the residue field of a local ring." Communications in Algebra 32, no. 2 (2004): 599-607.
Communications in Algebra