BCC-algebras with pseudo-valuations (Q2867601)
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: BCC-algebras with pseudo-valuations |
scientific article; zbMATH DE number 6241308
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | BCC-algebras with pseudo-valuations |
scientific article; zbMATH DE number 6241308 |
Statements
BCC-algebras with pseudo-valuations (English)
0 references
19 December 2013
0 references
weak pseudo-valuation
0 references
pseudo-metric induced by BCK-pseudo-valuation
0 references
BCK/BCC-valuation
0 references
A real-valued function \(\varphi\) defined on a BCK-algebra \(X\) is a pseudo-valuation if \(\varphi(0)=0\) and \(\varphi(x*y)\geq\varphi(x)+\varphi(y)\) for all \(x,y\in X\). If \(X\) is a BCC-algebra, then the second condition is replaced by \(\varphi((x*y)*z)\geq\varphi(x*z)-\varphi(y)\). Connections between pseudo-valuations on BCK-algebras and BCC-algebras (an important generalization of BCK-algebras) are described. Conditions for a real-valued function to be a BCK-pseudo-valuation are provided.
0 references
