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Commutative absolute subretracts

Part of: Modules, bimodules and ideals

Published online by Cambridge University Press:  09 April 2009

E. Jespers  and
M. M. Parmenter
E. Jespers
Affiliation:
Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John's, NewfoundlandCanadaA1C 5S7
M. M. Parmenter
Affiliation:
Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John's, NewfoundlandCanadaA1C 5S7
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Abstract

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Directly indecomposable absolute subretracts that are commutative Noetherian rings are described. This is an application of our main result characterizing unital directly indecomposable absolute subretracts which contain a maximal ideal with nonzero annihilator.

MSC classification

Secondary: 16D50: Injective modules, self-injective rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 1 , February 1993 , pp. 128 - 132
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, vol. 1 (Amer. Math. Soc., Providence, RI, 1961).Google Scholar
[2]Davey, B. A. and Kov´cs, L. G., ‘Absolute subretracts and weak injectives in congruence modular varieties’, Trans. Amer. Math. Soc. 297 (1986), 181–196.CrossRefGoogle Scholar
[3]Decruyenaere, F., Jespers, E. and Wauters, P., ‘On commutative principal ideal semigroup rings’, Semigroup Forum 43 (1991), 367–377.CrossRefGoogle Scholar
[4]Gardner, B. J. and Stewart, P. N., ‘Injective and weakly injective rings’, Canad. Math. Bull 31(1988), 487–494.CrossRefGoogle Scholar
[5]Jespers, E., ‘Special principal ideal rings and absolute subretracts’, Canad. Math. Bull. 34 (1991), 364–367.CrossRefGoogle Scholar
[6]McKenzie, R. N., McNulty, G. F. and Taylor, W. F., Algebras, Lattices, Varieties, vol. 1 (Wadsworth, Belmont, CA, 1987).Google Scholar
[7]Procesi, C., Rings with polynomial identities (Marcel Dekker, New York, 1973).Google Scholar
[8]Raphael, R., ‘Injective rings’, Comm. Algebra 1(1974), 403–414.CrossRefGoogle Scholar