We propose a slight weakening of the definitions of Artin monoids and Coxeter monoids. We study one ‘infinite series’ in detail.

Condition $(PWP)$ which was introduced in (Laan, V., {it Pullbacks and flatness properties of acts I}, Commun. Algebra, 29(2) (2001), 829-850), is related to flatness concept of acts over monoids. Golchin and Mohammadzadeh in ({it On Condition $(PWP_E)$}, Southeast Asian Bull. Math., 33 (2009), 245-256) introduced Condition $(PWP_E)$, such that Condition $(PWP)$ implies it, that is, Condition $...

It has been recently observed that fundamental aspects of the classical theory factorization can be greatly generalized by combining languages monoids and preorders. This led to various theorems on existence certain factorizations, herein called ⪯-factorizations, for ⪯-non-units a (multiplicatively written) monoid H endowed with preorder ⪯, where an element u∈H is ⪯-unit if u⪯1H⪯u ⪯-non-unit ot...

Various partial orders related to the structures of dual canonical monoids are investigated. It is shown that nilpotent variety a monoid equidimensional; its dimension found. in type A certain intervals Putcha poset isomorphic Renner matrices. The notion two-sided weak order on normal reductive introduced. criterion, terms maps, for covering relations have degree 2 that, unique equivariant divi...

We initiate the study of higher dimensional topological finiteness properties monoids. This is done by developing theory monoids acting on CW complexes. For this we establish foundations $M$-equivariant homotopy where $M$ a discrete monoid. projective $M$-CW complexes prove several fundamental results such as extension and lifting property, which use to Whitehead theorems. define left equivaria...

Bounded residuated lattice ordered monoids (R -monoids) are a common generalization of pseudo-BL-algebras and Heyting algebras, i.e. algebras of the non-commutative basic fuzzy logic (and consequently of the basic fuzzy logic, the Łukasiewicz logic and the non-commutative Łukasiewicz logic) and the intuitionistic logic, respectively. In the paper we introduce and study classes of filters of bou...

Divisibility monoids are a natural lattice-theoretical generalization of Mazurkiewicz trace monoids, namely monoids in which the distributivity of the involved divisibility lattices is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be commutations. Here, we show that every divisibility monoid admits an explicit finite transducer which allows to c...