Sets with \(B\)-action and linear algebra (Q1966134)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Sets with \(B\)-action and linear algebra |
scientific article; zbMATH DE number 1407087
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sets with \(B\)-action and linear algebra |
scientific article; zbMATH DE number 1407087 |
Statements
Sets with \(B\)-action and linear algebra (English)
0 references
27 February 2000
0 references
Let \(B\) be a Boolean ring. Any unital \(B\)-module \(M\) has a \(B\)-action given by \(\alpha [a,b]=\alpha a + (1+\alpha)b\) for all \(\alpha \in B\), \(a,b \in M\). It is shown that any set with \(B\)-action may be represented as a subset with \(B\)-action of a unital \(B\)-module. The result is extended to algebras with \(B\)-action and it is applied to if-then-else algebras over Boolean algebras.
0 references
Boolean ring
0 references
unital \(B\)-module
0 references
\(B\)-action
0 references
if-then-else algebra
0 references
