Related papers: Congruence Preserving Functions on Free Monoids
The semijoin operation is a fundamental operation of relational algebra that has been extensively used in query processing. Furthermore, semijoins have been used to formulate desirable properties of acyclic schemas; in particular, a schema…
We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…
For some monoids, we give a method of composing invertibility preserving maps associated to "partial involutions." Also, we define the notion of "determinants for finite dimensional algebras over a field." As examples, we give invertibility…
We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using two-way…
Let A be an alphabet and W be a set of words in the free monoid A*. Let S(W) denote the Rees quotient over the ideal of A* consisting of all words that are not subwords of words in W. We call a set of words W finitely based if the monoid…
Let $S$ be one of $\{aba,bcb\}$ and $\{aba, aca\}$, and let $w$ be an infinite square-free word over $\Sigma=\{a,b,c\}$ with no factor in $S$. Suppose that $f:\Sigma\rightarrow T^*$ is a non-erasing morphism. Word $f(w)$ is square-free if…
Graph products of monoids provide a common framework for direct and free products, and graph monoids (also known as free partially commutative monoids). If the monoids in question are groups, then any graph product is, of course, a group.…
We prove several results concerning finitely generated submonoids of the free monoid. These results generalize those known for free submonoids. We prove in particular that if $X=Y\circ Z$ is a composition of finite sets of words with $Y$…
Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational…
We study in general algebras Gratzer's notion of congruence preserving function, characterizing functions in terms of stability under inverse image of particular Boolean algebras of subsets generated from any subset of the algebra.…
An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all…
Let $k\geq 2$ be a square-free integer. We prove that the number of square-free integers $m\in [1,N]$ such that $(k,m)=1$ and $\mathbb{Q}(\sqrt[3]{k^2m})$ is monogenic is $\gg N^{1/3}$ and $\ll N/(\log N)^{1/3-\epsilon}$ for any…
We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study…
In this note we prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.
An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many…
A graph $G$ is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function $w$ is defined on its vertices. Then $G$ is $w$-well-covered if all maximal independent sets are of the same weight.…
A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For…
We consider algebras with one binary operation $\cdot$ and one generator ({\it monogenic}) and satisfying the left distributive law $a\cdot (b\cdot c)=(a\cdot b)\cdot (a\cdot c)$. One can define a sequence of finite left-distributive…
It is known that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite…
Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. They possess very strong regularity properties (reminiscent of the regularity…