A Note to the Definition of the LPi-Algebras

0405076 - UIVT-O 330181 RIV DE eng J - Journal Article
Cintula, Petr
A Note to the Definition of the LPi-Algebras.
[Poznámka k definici LPi-algeber.]
Soft Computing. Roč. 9, - (2005), s. 575-578. ISSN 1432-7643. E-ISSN 1433-7479
R&D Projects: GA ČR GD401/03/H047
Institutional research plan: CEZ:AV0Z10300504
Keywords : LPi-algebras * MV-algebras * Pi-algebras * PMV-algebras
Subject RIV: BA - General Mathematics
Impact factor: 0.538, year: 2005

The LPi-algebras have two sets of operations and reduct to one set is an MV-algebra and to the other one is a Pi-algebra. There arise a question: which additional identities (besides those of MV-algebra and Pi-algebra) has some algebra to fulfill in order to be an LPi-algebra? In this short paper we show that under certain definition of the Pi-algebra only one identity is sufficient. However the question whether this holds for an alternative definition of the Pi-algebra seems to be interesting open problem.

Jazyk LPi-algeber se sestává z dvou množin operací, redukt LPi-algebry na první z nich je MV-algebra a na té druhé Pi-algebra. Vyvstává otázka: jaké identity (mimo těch MV- a Pi-algebraických) definují LPi-algebry. V tomto krátkém článku ukážeme, že (za určitých okolností) stačí právě jedna. Ovšem otázka, zda tento fakt platí i pro alternetivní definici Pi-algeber je zajímavým otevřeným problémem.
Permanent Link: http://hdl.handle.net/11104/0125291