Vol. 61, No. 2, 1975

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Endomorphism rings of self-generators

Birge Huisgen-Zimmermann

Vol. 61 (1975), No. 2, 587–602

The group of R-homomorphisms HomR(M,A), where M, A are modules over a ring R, is, in a natural way, a module over the endomorphism ring S of M. Under certain weak assumptions on M, the following is true: HomR(M,) carries injective envelopes of R-modules into injective envelopes of S-modules iff M generates all its submodules. Modules of the latter type are called self-generators. For M a self-generator, HomR(M,) has additional properties concerning chain conditions and the socle. Many of the known results in this area, in particular those for M projective, are special cases of our main theorems.

Mathematical Subject Classification
Primary: 16A42, 16A42
Received: 15 May 1975
Published: 1 December 1975
Birge Huisgen-Zimmermann
Department of Mathematics
University of California Santa Barbara
Santa Barbara CA 93106-3080
United States