Multiplicative functions on the lattice of non-crossing partitions and free convolution.
Multiplicative lattices and -algebras
Multiplicative structures over sup-lattices
Multiplicatively idempotent semirings
Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive lattices....
Multipliers on a nearlattice
MV-algebras are categorically equivalent to a class of -semigroups
In the paper it is proved that the category of -algebras is equivalent to the category of bounded -semigroups satisfying the identity . Consequently, by a result of D. Mundici, both categories are equivalent to the category of bounded commutative -algebras.
MV-algebras with additive closure operators
Mодулярные структуры, в которых каждый элемент есть объединение циклов
N-anti-exchange closure operators
Natural continuity space structures on dual Heyting algebras
Natural dualities for varieties of distributive lattices with a quantifier
Natural extension of a congruence of a lattice to its lattice of convex sublattices
Let be a lattice. In this paper, corresponding to a given congruence relation of , a congruence relation on is defined and it is proved that 1. is isomorphic to ; 2. and are in the same equational class; 3. if is representable in , then so is in .
Natural generalization of some lattice theory concepts to partially ordered sets
Naturally Orderd Transformation Semigroups.
N-compact frames
We investigate notions of -compactness for frames. We find that the analogues of equivalent conditions defining -compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘-cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial -compactness form a much larger class, and better embody what ‘-compact frames’ should be. This latter property is expressible without reference...
ndependence of axioms for biordered sets.
Near lattices
Nearly disjoint sequences in convergence -groups
For an abelian lattice ordered group let be the system of all compatible convergences on ; this system is a meet semilattice but in general it fails to be a lattice. Let be the convergence on which is generated by the set of all nearly disjoint sequences in , and let be any element of . In the present paper we prove that the join does exist in .
Negaciones en retículos completos.
Negation in bounded commutative -monoids
The class of commutative dually residuated lattice ordered monoids (-monoids) contains among others Abelian lattice ordered groups, algebras of Hájek’s Basic fuzzy logic and Brouwerian algebras. In the paper, a unary operation of negation in bounded -monoids is introduced, its properties are studied and the sets of regular and dense elements of -monoids are described.