Nonstandard implication algebras
Note über den Operationskreis des Logikcalculs
Observation Space And Observables In Classical Mechanics
Observation space and observables in classical mechanics.
On a period of elements of pseudo-BCI-algebras
The notions of a period of an element of a pseudo-BCI-algebra and a periodic pseudo-BCI-algebra are defined. Some of their properties and characterizations are given.
On a periodic part of pseudo-BCI-algebras
In the paper the connections between the set of some maximal elements of a pseudo-BCI-algebra and deductive systems are established. Using these facts, a periodic part of a pseudo-BCI-algebra is studied.
On annihilators in BL-algebras
In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,0, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties...
On annihilators of BCK-algebras
On axiom systems of pseudo-BCK algebras.
On BE-semigroups.
On complete -algebras
On functions that cannot be mv-truth values in algebraic structures.
It is shown, in a general frame and playing with idempotency, that in order to have on a given lattice a Multiple Valued Logic preserving the lattice structure, the only t-norms and t-conorms allowing to modelize the truth values of a v b, a ^ b and a --> b are Min and Max, respectively, apart from ordinal sums.
On fuzzy -algebras
The fuzzification of (normal) -subalgebras is considered, and some related properties are investigated. A characterization of a fuzzy -algebra is given.
On fuzzy ideals in Hilbert algebras.
On ideal theory of hoops
In this paper, we define and characterize the notions of (implicative, maximal, prime) ideals in hoops. Then we investigate the relation between them and prove that every maximal implicative ideal of a -hoop with double negation property is a prime one. Also, we define a congruence relation on hoops by ideals and study the quotient that is made by it. This notion helps us to show that an ideal is maximal if and only if the quotient hoop is a simple MV-algebra. Also, we investigate the relationship...
On ideals and congruences in BCC-algebras
We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences.
On ideals in De Morgan residuated lattices
In this paper, we introduce a new class of residuated lattices called De Morgan residuated lattices, we show that the variety of De Morgan residuated lattices includes important subvarieties of residuated lattices such as Boolean algebras, MV-algebras, BL-algebras, Stonean residuated lattices, MTL-algebras and involution residuated lattices. We investigate specific properties of ideals in De Morgan residuated lattices, we state the prime ideal theorem and the pseudo-complementedness of the ideal...
On ideals in Hilbert algebras
On idempotent modifications of -algebras
The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of a group is subdirectly irreducible. For an -algebra we denote by and the idempotent modification, the underlying set or the underlying lattice of , respectively. In the present paper we prove that if is semisimple and is a chain, then is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.
On monadic quantale algebras: basic properties and representation theorems
Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.