A fundamental functional equation for vector lattices.
A Fundamental Functional Equation for Vector Lattices. (Short Communication).
A further investigation for Egoroff's theorem with respect to monotone set functions
In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.
A generalization of the prime radical of an ideal.
A glimpse of deductive systems in algebra
The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.
A groupoid characterization of Boolean algebras
We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.
A Hölder-type inequality for positive functionals on -algebras.
A hypervaluation of a ring onto a totally ordered non-cancellative semigroup without zero divisors.
A metrizable completely regular ordered space
We construct a completely regular ordered space such that is an -space, the topology of is metrizable and the bitopological space is pairwise regular, but not pairwise completely regular. (Here denotes the upper topology and the lower topology of .)
A non commutative generalization of -autonomous lattices
Pseudo -autonomous lattices are non-commutative generalizations of -autonomous lattices. It is proved that the class of pseudo -autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo -autonomous lattices can be described as their normal ideals.
A non-commutative generalization of -algebras
A normal form for some semigroups generated by idempotents
A note of a family of quasi-antiorders on semigroup
A note on approximation theorems
A note on Girard quantales
A note on good pseudo BL-algebras
Pseudo BL-algebras are a noncommutative extention of BL-algebras. In this paper we study good pseudo BL-algebras and consider some classes of these algebras.
A note on homogeneous lattices
A note on homomorphisms of Hilbert algebras.
A note on minimal and maximal ideals of ordered semigroups.
A note on noninterpretability in o-minimal structures
We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.