The aim of this paper is to study certain quasivarieties of left ample monoids. Left ample monoids are monoids of partial one–one mappings of sets closed under the operation α 7→ αα−1. The idempotents of a left ample monoid form a semilattice and have a strong influence on the structure of the monoid; however, a left ample monoid need not be inverse. Every left ample monoid has a maximum right ...

In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. this work, we extend classification to noncommutative monoid structures on surfaces. We prove that monoids are toric. also show how find all a toric surface. Every such structure is induced by comultiplication formula involving Demazure roots. give descriptions of opposite monoids, quotient b...

We compute the abelian kernels of some monoids of partial transformations. More precisely, the cases of the symmetric inverse monoid, monoids of order-preserving or order-reversing transformations, so as monoids of orientation-preserving or orientationreversing transformations are treated.

A large class of multiplicative submonoids of the natural numbers is presented, which includes congruence monoids as well as numerical monoids (by isomorphism). For monoids in this class, the important factorization property of finite elasticity is characterized.

Very little is known about the structure of intersection two $k$-generated monoids words, even for $k=3$. Here we investigate case $k$-maximal monoids, that is, whose basis cardinality $k$ cannot be non-trivially decomposed into at most words. We characterize in $3$-maximal monoids.

Algebraic structures sometimes need to be typed. For example, matrices over a ring form a ring, but the product is a only a partial operation: dimensions have to agree. Therefore, an easy way to look at matrices algebraically is to consider “typed rings”. We prove some “untyping” theorems: in some algebras (semirings, Kleene algebras, residuated monoids), types can be reconstructed from valid u...

We provide conditions on a monoidal model categoryM so that the category of commutative monoids in M inherits a model structure from M in which a map is a weak equivalence or fibration if and only if it is so inM. We then investigate properties of cofibrations of commutative monoids, rectification between E∞-algebras and commutative monoids, the relationship between commutative monoids and mono...

Kleene’s theorem on recognizable languages in free monoids is considered to be of eminent importance in theoretical computer science. It has been generalized into various directions, including trace and rational monoids. Here, we investigate divisibility monoids which are defined by and capture algebraic properties sufficient to obtain a characterization of the recognizable languages by certain...

We prove that there is a correspondence between self-similar group actions and the class of left cancellative right hereditary monoids satisfying the dedekind height property. The monoids in question turn out to be coextensive with the Zappa-Szép products of free monoids and groups, and the ideal structure of the monoid reflects properties of the group action. These monoids can also be viewed a...

For a monoid G the iterated multiplication problem is the computa tion of the product of n elements fromG By re ning known completeness arguments we show that as G varies over a natural series of important groups and monoids the iterated multiplication problems are complete for most natural low level complexity classes The completeness is with respect to rst order projections low level reductio...