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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 Tasmania G.P.O. Box 252-C Hobart, Tasmania 7001, Australia
P. N. Stewart
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University Halifax, 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

Information

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
2. Procesi, C., Rings with Polynomial Identity (Marcel Dekker, New York, 1973).Google Scholar
3. Raphaël, R, Injective rings Comm. Algebra 1 (1974), pp. 403–414.Google Scholar
4. Rowen, L. H., Polynomial Identities in Ring Theory (Academic Press, New York, 1980).Google Scholar