Normal \(C\)-algebras (Q2868579)
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: Normal \(C\)-algebras |
scientific article; zbMATH DE number 6239124
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Normal \(C\)-algebras |
scientific article; zbMATH DE number 6239124 |
Statements
17 December 2013
0 references
normal \(C\)-algebra
0 references
minimal prime ideal
0 references
multiplicative set
0 references
congruence
0 references
0 references
0.91570693
0 references
0 references
Normal \(C\)-algebras (English)
0 references
An algebra \((A,\wedge,\vee,')\) of type \((2,2,1)\) is a \(C\)-algebra if it satisfies the axiomsNEWLINENEWLINE(1) \(x''=x\),NEWLINENEWLINE (2) \((x\wedge y)'=x'\vee y'\),NEWLINENEWLINE (3) \((x\wedge y)\wedge z=x\wedge (y\wedge z)\),NEWLINENEWLINE (4) \(x\wedge (y\vee z)=(x\wedge y)\vee (x\wedge z)\),NEWLINENEWLINE (5) \((x\vee y)\wedge z=(x\wedge z)\vee (x'\wedge y\wedge z)\),NEWLINENEWLINE (6) \(x\vee (x\wedge y)=x\),NEWLINENEWLINE (7) \((x\wedge y)\vee (y\wedge x)=(y\wedge x)\vee (x\wedge y)\).NEWLINENEWLINEIn this paper, the notion of normal \(C\)-algebra is introduced and studied. It is shown that this class can be characterized in terms of minimal prime ideals. Also direct products and congruences of normal \(C\)-algebras are studied.
0 references
