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Projective Socles

Published online by Cambridge University Press:  20 November 2018

Patrick N. Stewart
Patrick N. Stewart*
Affiliation:
Department of Mathematics statistics and computing science dalhousie university halifax, nova scotia canada b3h 3j5
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Abstract

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Nicholson and Watters have recently investigated rings with projective socles and they have shown, among other things, that a ring R has a projective socle if and only if each matrix ring Mn(R), n > 1, has a projective socle. We generalize this result by showing that if S is an excellent extension of R, then the socle of R is projective if and only if the socle of S is projective. Examples of excellent extensions include, as well as matrix rings Mn(R), skew group rings R * G where G is a finite group and the order of G is invertible in R.

Keywords

16A5016A56
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 498 - 499
Copyright
Copyright © Canadian Mathematical Society 1989

References

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