18 research outputs found
Congruences on Menger algebras
We discuss some types of congruences on Menger algebras of rank , which
are generalizations of the principal left and right congruences on semigroups.
We also study congruences admitting various types of cancellations and describe
their relationship with strong subsets
Subtraction Menger algebras
Abstract characterizations of Menger algebras of partial -place functions
defined on a set and closed under the set-theoretic difference functions
treatment as subsets of the Cartesian product are given
The relation of semiadjacency of -semigroups of transformations
We consider two relations on a -semigroup of partial functions of a
given set: the inclusion of domains and the semiadjacencity (i.e., the
inclusion of the image of the first function into the domain of the second),
which characterized with an abstract point of view using the elementary system
of axioms, i.e., system conditions, recorded in the language narrow predicate
calculus with equality
Representations of -semigroups by multiplace functions
We describe the representations of -semigroups, i.e. groupoids with
binary associative operations, by partial -place functions and prove
that any such representation is a union of some family of representations
induced by Schein's determining pairs.Comment: 17 page
Menger algebras of -place opening operations
Algebraic properties of -place opening operations on a fixed set are
described. Conditions under which a Menger algebra of rank can be
represented by -place opening operations are found
Representations of Menger -semigroups by multiplace functions
Investigation of partial multiplace functions by algebraic methods plays an
important role in modern mathematics were we consider various operations on
sets of functions, which are naturally defined. The basic operation for
-place functions is an -ary superposition , but there are some
other naturally defined operations, which are also worth of consideration. In
this paper we consider binary Mann's compositions \op{1},...,\op{n} for
partial -place functions, which have many important applications for the
study of binary and -ary operations. We present methods of representations
of such algebras by -place functions and find an abstract characterization
of the set of -place functions closed with respect to the set-theoretic
inclusion