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Sets with B -action and linear algebra

Stokes, T. (1998) Sets with B -action and linear algebra. Algebra Universalis, 39 (1-2). pp. 31-43.

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Let B be a Boolean ring. Any unital B-module M has a B-action given by α[a,b]=αa+(1+α)b for all α∈B,a,b,∈M. We show that any set with B-action may be represented as a subset with B-action of a unital B-module. We extend this to algebras with B-action and apply it to if-then-else algebras over Boolean algebras by viewing them as semilattices with B-action.

Item Type: Journal Article
Murdoch Affiliation(s): School of Mathematical and Physical Sciences
Publisher: Springer
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