A Representation of Lattice Effect Algebras by Means of Right Near Semirings with Involution

Chajda, Ivan; Länger, Helmut

doi:10.1007/s10773-016-3191-8

Record link:

https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-2739
http://hdl.handle.net/20.500.12708/324

Title:

A Representation of Lattice Effect Algebras by Means of Right Near Semirings with Involution

Citation:

Chajda, I., & Länger, H. (2017). A Representation of Lattice Effect Algebras by Means of Right Near Semirings with Involution. International Journal of Theoretical Physics. https://doi.org/10.1007/s10773-016-3191-8

Publisher DOI:

10.1007/s10773-016-3191-8

CatalogPlus:

AC11361199

Publication Type:

Article - Original Research Article

Language:

English

Authors:

Chajda, Ivan
Länger, Helmut

Organisational Unit:

E104 - Institut für Diskrete Mathematik und Geometrie

Journal:

International Journal of Theoretical Physics

ISSN:

0020-7748

Date (published):

Dec-2017

Publisher:

Springer

Peer reviewed:

Yes

Keywords:

Effect algebra; Lattice effect algebra; Right near semiring; Antitone involution; Effect near semiring

Abstract:

Since every lattice effect algebra decomposes into blocks which are MV-algebras and since every MV-algebra can be represented by a certain semiring with an antitone involution as shown by Belluce, Di Nola and Ferraioli, the natural question arises if a lattice effect algebra can also be represented by means of a semiring-like structure. This question is answered in the present paper by establishing a one-to-one correspondence between lattice effect algebras and certain right near semirings with an antitone involution.

License:

CC BY 4.0