On sets related to maximal clones

Yeni Susanti; Klaus Denecke

Displaying similar documents to “On sets related to maximal clones”

On $☆$ - associated comonotone functions

Ondrej Hutník, Jozef Pócs (2018)

Kybernetika

Similarity:

We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to $+$ -associatedness of functions (as proved by Boczek and Kaluszka), but also to their $☆$ -associatedness with $☆$ being an arbitrary...

Regular elements and Green's relations in Menger algebras of terms

Klaus Denecke, Prakit Jampachon (2006)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Defining an (n+1)-ary superposition operation $S^{n}$ on the set $W_{τ} (X_{n})$ of all n-ary terms of type τ, one obtains an algebra $n - c l o n e τ : = (W_{τ} (X_{n}); S^{n}, x_{1}, . . ., x_{n})$ of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation $S^{n}$ there are different possibilities to define binary associative operations on the set $W_{τ} (X_{n})$ and on the cartesian power $W_{τ} {(X_{n})}^{n}$ . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative...

On the number of finite algebraic structures

Erhard Aichinger, Peter Mayr, R. McKenzie (2014)

Journal of the European Mathematical Society

Similarity:

We prove that every clone of operations on a finite set $A$ , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting $R$ for some finitary relation $R$ over $A$ . It follows that for a fixed finite set $A$ , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra...

On semigroups of $σ$ -endomorphisms

Iwanik, Anzelm

Similarity:

$ℱ$ -hypercyclic and disjoint $ℱ$ -hypercyclic properties of binary relations over topological spaces

Marko Kostić (2020)

Mathematica Bohemica

Similarity:

We examine various types of $ℱ$ -hypercyclic ( $ℱ$ -topologically transitive) and disjoint $ℱ$ -hypercyclic (disjoint $ℱ$ -topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples.

Expansions of binary recurrences in the additive base formed by the number of divisors of the factorial

Florian Luca, Augustine O. Munagi (2014)

Colloquium Mathematicae

Similarity:

We note that every positive integer N has a representation as a sum of distinct members of the sequence ${d (n!)}_{n \geq 1}$ , where d(m) is the number of divisors of m. When N is a member of a binary recurrence $u = {u ₙ}_{n \geq 1}$ satisfying some mild technical conditions, we show that the number of such summands tends to infinity with n at a rate of at least c₁logn/loglogn for some positive constant c₁. We also compute all the Fibonacci numbers of the form d(m!) and d(m₁!) + d(m₂)! for some positive integers m,m₁,m₂. ...

On a special class of left-continuous uninorms

Gang Li (2018)

Kybernetika

Similarity:

This paper is devoted to the study of a class of left-continuous uninorms locally internal in the region $A (e)$ and the residual implications derived from them. It is shown that such uninorm can be represented as an ordinal sum of semigroups in the sense of Clifford. Moreover, the explicit expressions for the residual implication derived from this special class of uninorms are given. A set of axioms is presented that characterizes those binary functions $I : {[0, 1]}^{2} \to [0, 1]$ for which a uninorm $U$ of this special...

Algorithm for the complement of orthogonal operations

Iryna V. Fryz (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a $k$ -tuple of orthogonal $n$ -ary operations, where $k < n$ , to an $n$ -tuple of orthogonal $n$ -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a $k$ -tuple of orthogonal $n$ -ary operations to an $n$ -tuple of orthogonal $n$ -ary operations and an algorithm for complementing a $k$ -tuple of orthogonal $k$ -ary operations to an $n$ -tuple of orthogonal $n$ -ary operations. Also...

Inverses of generators of nonanalytic semigroups

Ralph deLaubenfels (2009)

Studia Mathematica

Similarity:

Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup ${e^{t A}}_{t \geq 0}$ . It is shown that $A^{- 1}$ generates an $O (1 + τ) A {(1 - A)}^{- 1}$ -regularized semigroup. Several equivalences for $A^{- 1}$ generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of ${e^{t A}}_{t \geq 0}$ , on subspaces, for $A^{- 1}$ generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate...

$𝒯$ -Prime Subsets in Semigroups

Bedřich Pondělíček (1975)

Matematický časopis

Similarity: