Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T00:09:50.772Z Has data issue: false hasContentIssue false
  • English
  • Français

Extension and amalgamation in rings

Published online by Cambridge University Press:  14 November 2011

J. Renshaw
J. Renshaw
Affiliation:
Department of Pure Mathematics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland
Get access Rights & Permissions [Opens in a new window]

Synopsis

It is proved that if a ring R has the extension property in containing ringSi, then the amalgam [R; Si,] is strongly embeddable. Using a result of P. M. Cohn, a necessary and sufficient condition for a ring to be an amalgamation base is then given. It is also shown that R is a level subring of a ring S if and only if S/R is flat. From this, a classical result of P. M. Cohn on flat amalgams is proved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 1-2 , 1986 , pp. 103 - 115
Copyright
Copyright © Royal Society of Edinburgh 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bergman, G. M. and Dicks, W.. Universal derivations and universal ring constructions. Pacific J. Math. 79 (1978), 293–337.CrossRefGoogle Scholar
2Cohn, P. M.. On the free product of associative rings. Math. Z. 71 (1959), 380–398.CrossRefGoogle Scholar
3Fieldhouse, D. J.. Pure theories. Math. Ann. 184 (1969), 1–18.CrossRefGoogle Scholar
4Hall, T. E.. Representation extension and amalgamation for semigroups. Quart. J. Math. Oxford Ser. (2) 29 (1978), 309–334.CrossRefGoogle Scholar
5Howie, J. M.. Epimorphisms and amalgamations: A survey of recent progress. Proc. Conf. on Semigroups, Szeged, 1981 (to appear).Google Scholar
6Renshaw, J.. Extension and amalgamation in monoids and semigroups. Proc. London Math. Soc. (3) (to appear).CrossRefGoogle Scholar
7Renshaw, J.. Flatness and amalgamation in monoids. J. London Math. Soc. (2) (to appear).CrossRefGoogle Scholar
8Rotman, J. J., An Introduction to homological algebra (London: Academic Press, 1979).Google Scholar