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Injective and Weakly Injective Rings

Published online by Cambridge University Press:  20 November 2018

B. J. Gardner  and
P. N. Stewart
B. J. Gardner
Affiliation:
Mathematics Department, University of TasmaniaG.P.O. Box 252-C Hobart, Tasmania 7001, Australia
P. N. Stewart
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie UniversityHalifax, Nova Scotia B3H 3J5, Canada
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Abstract

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Let V be a variety of rings and let A ∊ V. The ring A is injective in V if every triangle

with C ∊ V, m a monomorphism and f a homomorphism has a commutative completion as indicated. A ring which is injective in some variety (equivalently, injective in the variety it generates) is called injective. When only triangles with f surjective are considered we obtain the notion of weak injectivity. Directly indecomposable injective and weakly injective rings are classified.

Keywords

16A5208B30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 487 - 494
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Davey, B. A. and L. G. Kovács, Absolute subretracts and weak injectives in congruence modular varieties Trans. A.M.S. 297(1986), pp. 181–196.Google Scholar
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4. Rowen, L. H., Polynomial Identities in Ring Theory (Academic Press, New York, 1980).Google Scholar