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...
Let be an infinite cardinal. Let be the class of all lattices which are conditionally -complete and infinitely distributive. We denote by the class of all lattices such that is infinitely distributive, -complete and has the least element. In this paper we deal with direct factors of lattices belonging to . As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class .
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.
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.
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.
Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite distributive lattices in terms of the core label order...
We present a construction of finite distributive lattices with a given skeleton. In the case of an H-irreducible skeleton K the construction provides all finite distributive lattices based on K, in particular the minimal one.
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.
Gli insiemi parziali sono coppie di sottoinsiemi di , dove . Gli insiemi parziali su costituiscono una DMF-algebra, ossia un'algebra di De Morgan in cui la negazione ha un solo punto fisso. Dimostriamo che ogni DMF-algebra è isomorfa a un campo di insiemi parziali. Utilizzando gli insiemi parziali su come aperti, introduciamo il concetto di spazio topologico parziale su . Infine associamo ad ogni DMF-algebra uno spazio topologico parziale i cui clopen compatti costituiscono un campo d'insiemi...