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Completely Faithful Modules and Self-Injective Rings

Published online by Cambridge University Press:  22 January 2016

Goro Azumaya
Goro Azumaya*
Affiliation:
University of Massachusetts and Indiana University
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A left module over a ring Λ is called completely faithful if Λ is a sum of those left ideals which are homomorphic images of M. The notion was first introduced by Morita [9], and he proved, among others, the following theorem which plays a basic role in his theory of category-isomorphisms: if a Λ-module M is completely faithful, then M is finitely generated and projective with respect to the endomorphism ring Γ of M and Λ coincides with the endomorphism ring of Λ-module M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 697 - 708
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

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