Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

Title:

Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

Creator:

Kühr, Jan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:734dba3c-a31f-414f-aa43-46487a2a7e02
uuid:734dba3c-a31f-414f-aa43-46487a2a7e02

Subject:

pseudo $MV$-algebra, $DR\ell $-monoid, and generalized pseudo effect algebra

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We deal with unbounded dually residuated lattices that generalize pseudo $MV$-algebras in such a way that every principal order-ideal is a pseudo $MV$-algebra. We describe the connections of these generalized pseudo $MV$-algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo $MV$-algebra $A$ by means of the positive cone of a suitable $\ell $-group $G_A$. We prove that the lattice of all (normal) ideals of $A$ and the lattice of all (normal) convex $\ell $-subgroups of $G_A$ are isomorphic. We also introduce the concept of Archimedeanness and show that every Archimedean generalized pseudo $MV$-algebra is commutative.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

395-415

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:2

Harvested from:

CDK

Metadata only:

false