Idempotent-determined congruences on inverse semigroups.
Idempotents in completely PO semigroups.
Identities which imply that a ring is Boolean
IF-filters of pseudo-BL-algebras
Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF- filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of IF-filters and direct product of IF-filters are studied.
Images homomorphes, ordonnées en treillis des demi-groupes ordonnés
Imbedding locally convex lattices into compact lattices
Implication algebras
We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties....
Implication and equivalential reducts of basic algebras
A term operation implication is introduced in a given basic algebra and properties of the implication reduct of are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of and, if this partial order is linear, the algebra can be reconstructed by means of...
Implications partielles dans un contexte
Nous présentons une extension de la théorie des implications entre attributs binaires aux implications partielles. A partir de données expérimentales on s'intéresse non seulement aux implications (globales), mais aussi aux «implications avec quelques contre exemples». Les implications partielles offrent une possibilité d'extraire des informations supplémentaires. Elles permettent de «modéliser» la fréquence relative d'une implication, non-valide pour toutes les données, et donnent par conséquent...
Implicative commutative semigroups are equivalent to a class of BCK algebras.
Implicative hyper -algebras
In this note we first define the notions of (weak, strong) implicative hyper -algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper -ideals. Also we obtain some relations between these notions and (weak) implicative hyper -ideals. Finally, we study the implicative hyper -algebras of order 3, in particular we obtain a relationship between the positive implicative...
Implicative ideals of BCK-algebras based on the fuzzy sets and the theory of falling shadows.
In memory of Jaroslav Ježek
Incidence algebras and algebraic fundamental group.
Incidence structures and closure spaces
Incidence structures of independent sets
Incidence structures of type
Every incidence structure (understood as a triple of sets , ) admits for every positive integer an incidence structure where () consists of all independent -element subsets in () and is determined by some bijections. In the paper such incidence structures are investigated the ’s of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets and .
Incomparably continuable sets of semilattices
A finite set of finite semilattices is said to be incomparably continuable if it can be extended to an infinite set of pairwise incomparable (with respect to embeddability) finite semilattices. After giving some simple examples we show that the set consisting of the four-element Boolean algebra and the four-element fork is incomparably continuable.
Indecomposable matrices over a distributive lattice
In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set of all fully indecomposable matrices as a subsemigroup of the semigroup of all Hall matrices over the lattice are given.
Independence in a set with orthogonality