We describe the local structure of an irreducible algebraic monoid M at an idempotent element e. When e is minimal, we show that M is an induced variety over the kernel MeM (a homogeneous space) with fibre the two-sided stabilizer Me (a connected affine monoid having a zero element and a dense unit group). This yields the irreducibility of stabilizers and centralizers of idempotents when M is n...

We show that if (M,⊗, I) is a monoidal model category then REnd M (I) is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2-monoid.

We state a simple condition on a rational subset X of a free monoid B for the existence of a sequential function that is a one-to-one mapping of some free monoid A onto X. As a by-product we obtain new sequential bijections of a free monoid onto another.

The Neron-Severi group of divisor classes modulo algebraic equivalence on a smooth algebraic surface is often not difficult to calculate, and has classically been studied as one of the fundamental invariants of the surface. A more difficult problem is the determination of those divisor classes which can be represented by effective divisors; these divisor classes form a monoid contained in the N...

There is a well-known correspondence between varieties of algebras and fully invariant congruences on the appropriate term algebra. A special class of varieties are those which are balanced, meaning they can be described by equations in which the same variables appear on each side. In this paper, we prove that the above correspondence, restricted to balanced varieties, leads to a correspondence...

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 ...

We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we prove that the context-free language L1 ∗ = {ab : n ≥ 1}∗ can not be recognized by any rational monoid automaton over a finitely generated permutable monoid. We show that the class of la...

We described in [M1] a monoid b G, the face monoid, acting on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group G. We found in [M5] two natural extensions of the action of the Kac-Moody group G on its building Ω to actions of the face monoid b G on the building Ω....

in this paper $s$ is a monoid with a left zero and $a_s$ (or $a$) is a unitary right $s$-act. it is shown that a monoid $s$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $s$-act is quasi-projective. also it is shown that if every right $s$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...

We show that if (M,⊗, I) is a monoidal model category then REnd M (I) is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2-monoid.