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Azumaya’s Canonical Module and Completions of Algebras
Published online by Cambridge University Press: 22 January 2016
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We are concerned with an algebra S over a commutative ring. Precisely S is a non-commutative ring with identity which is also a finitely generated unital R module such that r(xy) = (rx)y = x(ry) for r in R and x, y ∈ S. In section one, we assume A is a commutative, Artinian ring. Following Goro Azumaya (see (1, p. 273)), we define the canonical module F of A to be the injective hull of A modulo the Jacobson radical of A i.e. F = I(A/J(A)).
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1973
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