ACTA issues

Varieties of lattice effect algebras generated by four-element members

Ivan Chajda, Radomír Halaš

Acta Sci. Math. (Szeged) 74:1-2(2008), 49-64

Abstract. It has been recently shown [3] that the lattice effect algebras can be treated as a subvariety of the variety of so-called basic algebras. The main goal of this paper is to describe the variety of basic algebras generated by the horizontal sum of two 3-element MV-chains. It is shown that this variety is modulo the variety of distributive lattice effect algebras characterized by a unique simple identity.

AMS Subject Classification (1991): 08A30, 08B10

Keyword(s): Lattice effect algebra, basic algebra, antitone involution, variety

Received April 26, 2007, and in revised form November 22, 2007. (Registered under 6002/2009.)