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Representation extensions and amalgamation bases in rings

Part of: Chain conditions, growth conditions, and other forms of finiteness

Published online by Cambridge University Press:  26 February 2010

Kunitaka Shoji
Kunitaka Shoji
Affiliation:
Department of Mathematics, Shimane University, Matsue, Shimane, 690, Japan.
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Abstract

The main purposes of this paper are to investigate ℤ-injective rings with the representation extension property and its dual, to give a necessary and sufficient condition for a ℤ-injective ring to be an amalgamation base in the class of all rings and to determine structure of ℤ-injective Noetherian rings which are amalgamation bases. Further, in the class of all commutative rings, it is shown that a commutative ring has the representation extension property, if, and only if, it is an amalgamation base.

MSC classification

Secondary: 16P40: Noetherian rings and modules
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 394 - 400
Copyright
Copyright © University College London 1994

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References

1.Bass, H.. Finitistic dimension and a homological generalization of semiprimary rings. Trans. Amer. Soc, 95 (1960), 466–488.CrossRefGoogle Scholar
2.Cohn, P. M.. On the free product of associative rings. Math. Zeit., 71 (1959), 380–398.CrossRefGoogle Scholar
3.Dlab, V.. On a characterization of primary abelian groups of bounded order. J. London Math. Soc, 36 (1961), 139–144.CrossRefGoogle Scholar
4.Eilenberg, S. and Nakayama, T.. The dimension of modules and algebras. II, Nagoya Math. J., 9 (1955), 1–16.CrossRefGoogle Scholar
5.Fuchs, L.. Infinite abelian groups, Vol. I (Academic Press, New York, 1970).Google Scholar
6.Hall, T. E.. Representation extension and amalgamation for semigroups. Quart. J. Math. Oxford, Ser. (2), 29 (1978), 309–334.CrossRefGoogle Scholar
7.Kato, T., Torsionless modules. Tohoku Math. J., 20 (1968), 234–243.CrossRefGoogle Scholar
8.Nakayama, T.. On Frobeniusean algebras. II. Ann. Math., 42 (1941), 1–21.CrossRefGoogle Scholar
9.Renshaw, J.. Extension and amalgamation in rings. Proc. Royal Soc. Edinburgh, 102 (1986), 103–115.CrossRefGoogle Scholar
10.Rotman, J. J.. An introduction to homological algebra (Academic Press, 1979).Google Scholar
11.Shoji, K.. Amalgamation bases for semigroups. Math. Japonica, 35 (1990), 473–483.Google Scholar