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Discrete structure spaces of ƒ-rings

Published online by Cambridge University Press:  09 April 2009

Peter D. Colville
Peter D. Colville
Affiliation:
Monash University, Clayton, Victoria 3168, Australia The Ballarat Institute of Advanced Education, Ballarat, Australia
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Birkhoff and Pierce [2] introduced the concept of an ƒ-ring and showed that an l-ring is an f-ring if and only if it is a subdirect product of totallyordered rings. An l-ideal of an f-ring R is an algebraic ideal which is at the same time a lattice ideal of R. Structure spaces (i.e. sets of prime ideals endowed with the so-called hull-kernel or Stone topology) for ordinary rings have been studied by many authors. In this paper we consider certain analogues for ƒ-rings, and give characterisations of ƒ-rings for which these structure spaces are discrete.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 1 , August 1974 , pp. 104 - 110
Copyright
Copyright © Australian Mathematical Society 1974

References

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