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Representation and extension of semiprime rings

Published online by Cambridge University Press:  09 April 2009

G. Davis
G. Davis
Affiliation:
Department of Mathematics La Trobe University Bundoora, Vic. 3083, Australia
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In many respects the theory of semi-prime rings (i.e. rings without proper nilpotents) is similar to that for lattice-ordered groups. In this paper semi-prime rings are faithfully represented as subrings of continuous global sections of sheaves of integral domains with Boolean base spaces. This representation allows a simple description of a particular extension of a semi-prime ring as the corresponding ring of all continuous global sections. The ideals in a semi-prime ring R that give rise to the stalks in the sheaf representation are then characterized when R is projectable. Finally equivalent conditions are given for a semi-prime ring R to satisfy a condition, that in the case of lattice-groups, was termed “weak projectability” by Spirason and Strzelecki [8]. Some of the results that are common to semi-prime rings and lattice-groups (and semi-prime semigroups) have been extended to certain universal algebras by Davey [3].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 3 , May 1973 , pp. 353 - 365
Copyright
Copyright © Australian Mathematical Society 1973

References

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