Derivations of MV-algebras.
Direct product decompositions of bounded commutative residuated -monoids
The notion of bounded commutative residuated -monoid (-monoid, in short) generalizes both the notions of -algebra and of -algebra. Let be a -monoid; we denote by the underlying lattice of . In the present paper we show that each direct...
Direct product decompositions of pseudo effect algebras
Direct product decompositions of pseudo -algebras
In this paper we deal with the relations between the direct product decompositions of a pseudo -algebra and the direct product decomposicitons of its underlying lattice.
Direct product factors in GMV-algebras
Direct summands and retract mappings of generalized -algebras
In the present paper we deal with generalized -algebras (-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, -algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of -algebras. The relations between -algebras and lattice ordered groups are essential for this investigation.
Directoids with sectionally antitone involutions and skew MV-algebras
It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras.
Distinguished extensions of an -algebra
Distributivity of bounded lattices with sectionally antitone involutions
We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.
DRl-semigroups and -algebras