A note to the definition of the ŁΠ-algebras

Abstract

The ŁP-algebras are interesting algebraic structures. They were introduced by Esteva, Godo, and Montagna. These algebras are closely related to the wellknown MV-algebras and P-algebras. They have two sets of operations and reduct to one set is an MV-algebra and to the other one is a P-algebra.Other important reducts of ŁP-algebras are so-called PŁ-algebras (an MV-algebras enriched with product connective) and P $ -algebras (P-algebras with additional involutive negation).The definition of ŁP-algebras is based on its MValgabraic reduct and the additional identities. In this paper we present how to base this definition on the other reducts we mention above. We present minimal sets of conditions which has to be added to the defining conditions of those reducts in order to obtain ŁP-algebras.Definition 2. A MV-algebra is a structure L = ðL; È; À Ł ; 0 L Þ such that: Soft Comput (2005) 9: 575-578