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Additive Divisibility in Compact Topological Semirings

Published online by Cambridge University Press:  20 November 2018

P. H. Karvellas
P. H. Karvellas*
Affiliation:
Department of Electrical Engineering, University of Alberta, Edmonton, Alberta
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A topological semiring (S, + , ·) is a nonempty Hausdorff space S on which are defined continuous and associative operations, termed addition (+) and multiplication (·), such that the multiplication distributes over addition from left and right. The additive semigroup (S, +) need not be commutative.

We prove that the set A of additively divisible elements of a compact semiring S is a two-sided multiplicative ideal, containing the set E[+] of additive idempotents, with the property that (A.S) ∪ (S.A) ⊂ E[+].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 593 - 599
Copyright
Copyright © Canadian Mathematical Society 1974

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