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Localizations of essential extensions

Published online by Cambridge University Press:  20 January 2009

K. R. Goodearl  and
D. A. Jordan
K. R. Goodearl
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, U.S.A.
D. A. Jordan
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, England
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In an earlier paper [4] we considered the question of whether an injective module E over a noncommutative ring R remains injective after localization with respect to a denominator set X in R. A related question is whether, given an essential extension N of an R-module M, the localization N[X–1] must be an essential extension of M[X–1]. In [1] it is shown that if R is left noetherian and X is central in R, then localization at X preserves both injectivity and essential extensions of left R-modules and, hence, preserves injective hulls and minimal injective resolutions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 243 - 247
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

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