This paper concerns the monoid Hecke algebras H introduced by Louis Solomon. We determine explicitly the unities of the orbit algebras associated with the two-sided action of the Weyl group W . We use this to: 1. find a description of the irreducible representations of H, 2. find an explicit isomorphism between H and the monoid algebra of the Renner monoid R, 3. extend the Kazhdan-Lusztig invol...

We investigate the relationship between regular languages and syntactic monoid size. In particular, we consider the transformation monoids of n-state (minimal) deterministic finite automata. We show tight upper bounds on the syntactic monoid size, proving that an nstate deterministic finite automaton with singleton input alphabet (input alphabet with at least three letters, respectively) induce...

A given monoid usually admits many presentations by generators and relations the notion of Tietze equivalence characterizes when two describe same monoid: it is case one can transform presentation into other using families so-called transformations. The goal this article to provide an abstract geometrical understanding well-known fact, constructing a model structure on category presentations, i...

Primary and strongly primary monoids domains play a central role in the ideal factorization theory of commutative domains. It is well-known that satisfying ascending chain condition on divisorial ideals (e.g., numerical monoids) are primary; multiplicative monoid non-zero elements one-dimensional local domain it if Noetherian. In present paper, we focus study additive submonoids non-negative ra...