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Global dimensions of right coherent rings with left Krull dimension

Published online by Cambridge University Press:  17 April 2009

Mark L. Teply
Mark L. Teply
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53209, United States of America
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Abstract

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The weak global dimension of a right coherent ring with left Krull dimension α ≥ 1 is found to be the supremum of the weak dimensions of the β-critical cyclic modules, where β < α. If, in addition, the mapping I → assl gives a bijection between isomorphism classes on injective left R-modules and prime ideals of R, then the weak global dimension of R is the supremum of the weak dimensions of the simple left R-modules. These results are used to compute the left homological dimension of a right coherent, left noetherian ring. Some analogues of our results are also given for rings with Gabriel dimension.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 2 , April 1989 , pp. 215 - 223
Copyright
Copyright © Australian Mathematical Society 1989

References

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