Every C*-algebra gives rise to an effect module and a convex space of states, which are connected via Kadison duality. We explore this duality in several examples, where the C*-algebra is equipped with the structure of a finite-dimensional Hopf algebra. When the Hopf algebra is the function algebra or group algebra of a finite group, the resulting state spaces form convex monoids. We will prove...

This article is the second of two presenting a new approach to left adequate monoids. In the first, we introduced the notion of being T -proper, where T is a submonoid of a left adequate monoid M . We showed that the free left adequate monoid on a set X is X∗-proper. Further, any left adequate monoid M has an X∗-proper cover for some set X , that is, there is an X∗proper left adequate monoid M̂ ...

In this paper we construct a free resolution for a free partially commutative monoid and with its help prove the Husainov’s Conjecture. We follow the ideas of D. Cohen who built in [3] a resolution for the so-called graph product of groups, given resolutions for factors. The presentation of the graph product with the help of direct and free amalgamated products played the leading role at that. ...

In this paper we relate two generalisations of the finite monoid recognisers of automata theory for the study of circuit complexity classes: Boolean spaces with internal monoids and typed monoids. Using the setting of stamps, this allows us to generalise a number of results from algebraic automata theory as it relates to Büchi’s logic on words. We obtain an Eilenberg theorem, a substitution pri...

Let R be a ring and C a class of right R-modules closed under finite direct sums. If we suppose that C has a set of representatives, that is, a set V(C) ⊆ C such that every M ∈ C is isomorphic to a unique element [M ] ∈ V(C), then we can view V(C) as a monoid, with the monoid operation [M1] + [M2] = [M1 ⊕M2]. Recent developments in the theory of commutative monoids (e.g., [4], [15]) suggest tha...

‎There is a flatness property of acts over monoids called Condition $(PWP)$ which‎, ‎so far‎, ‎has received‎ ‎much attention‎. ‎In this paper‎, ‎we introduce Condition GP-$(P)$‎, ‎which is a generalization of Condition $(PWP)$‎. ‎Firstly‎, ‎some  characterizations of monoids by Condition GP-$(P)$ of their‎ ‎(cyclic‎, ‎Rees factor) acts are given‎, ‎and many known results are generalized‎. ‎More...

A property P of string-rewriting systems is called modular if the disjoint union R 1 R 2 of two string-rewriting systems R 1 and R 2 has this property if and only if R 1 and R 2 both have this property. Analogously, a property P of monoids is modular if the free product M 1 M 2 of two monoids M 1 and M 2 has this property if and only if M 1 and M 2 both have this property. Since the string-rewr...

Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. In this paper we introduce a new property of acts over monoids, called U-WPF which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. We also show that regu...

laan in (ph.d thesis, tartu. 1999) introduced the principal weak form of condition $(p)$ as condition $(pwp)$ and gave some characterization of monoids by this condition of their acts. in this paper first we introduce condition (g-pwp), a generalization of condition $(pwp)$ of acts over monoids and then will give a characterization of monoids when all right acts satisfy this condition. we also ...

We sketch a theory of divisibility and factorization in topological monoids, where finite products are replaced by convergent products. The algebraic case can then be viewed as the special case of discretely topologized topological monoids. We define the topological factorization monoid, a generalization of the factorization monoid for algebraic monoids, and show that it is always topologically...