A characterization of ordered groups by means of segments
A characterization of polarities whose lattice of polars is Boolean
A characterization of polarities whose polar lattice is orthomodular
A characterization of quantic quantifiers in orthomodular lattices.
A characterization of regular le-semigroups.
A characterization of semilattices
A characterization of subgroup lattices of finite abelian groups.
A characterization of tolerance-distributive tree semilattices
A characterization of uninorms on bounded lattices via closure and interior operators
Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.
A characterization of well-orders
A C(K) Banach space which does not have the Schroeder-Bernstein property
We construct a totally disconnected compact Hausdorff space K₊ which has clopen subsets K₊” ⊆ K₊’ ⊆ K₊ such that K₊” is homeomorphic to K₊ and hence C(K₊”) is isometric as a Banach space to C(K₊) but C(K₊’) is not isomorphic to C(K₊). This gives two nonisomorphic Banach spaces (necessarily nonseparable) of the form C(K) which are isomorphic to complemented subspaces of each other (even in the above strong isometric sense), providing a solution to the Schroeder-Bernstein problem for Banach spaces...
A class of congruences on a posemigroup.
A class of -preduals which are isomorphic to quotients of
For every countable ordinal α, we construct an -predual which is isometric to a subspace of and isomorphic to a quotient of . However, is not isomorphic to a subspace of .
A class of multiplicative lattices
We study the multiplicative lattices which satisfy the condition for all . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group or . A sharp lattice localized at its maximal elements are totally ordered sharp lattices. The converse is true if has finite character.
A classification of rational languages by semilattice-ordered monoids
We prove here an Eilenberg type theorem: the so-called conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilattice-ordered monoids. Taking complements of members of a conjunctive variety of languages we get a so-called disjunctive variety. We present here a non-trivial example of such a variety together with an equational characterization of the corresponding pseudovariety.
A combinatorial theorem on the existence of a separating element and its applications to sequences and -derivations of measures
A comment on Balbes' representation theorem for distributive quasi-lattices
A common abstraction of boolean rings and lattice ordered groups
A common approach to directoids with an antitone involution and D-quasirings
We introduce the so-called DN-algebra whose axiomatic system is a common axiomatization of directoids with an antitone involution and the so-called D-quasiring. It generalizes the concept of Newman algebras (introduced by H. Dobbertin) for a common axiomatization of Boolean algebras and Boolean rings.
A Complete Boolean Algebra without Homogeneous or Rigid Factors.