The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if and only if it is in the quasivariety generated by the monoid obtained by adjoining an identity to the two-element left zero semigroup. We prove that this quas...

In this paper we show that ωBand ωS-regular languages satisfy the following separation-type theorem If L1, L2 are disjoint languages of ω-words both recognised by ωB(resp. ωS)automata then there exists an ω-regular language Lsep that contains L1, and whose complement contains L2. In particular, if a language and its complement are recognised by ωB(resp. ωS)automata then the language is ω-regula...

Many important families of regular languages have effective characterizations in terms of syntactic monoids or syntactic semigroups (see e.g. [1]). Definition of the syntactic monoid (resp. syntactic semigroup) of a language L ⊆ X * (resp. a language L ⊆ X +) over an alphabet X requires regarding L as a subset of the free monoid X * (resp. free semigroup X +). On the other hand tree languages h...

Are all finitely generated projective k[t1, . . . , td]-modules free for an arbitrary field k and arbitrary d ∈ N? This question, set in Serre’s famous paper FAC in 1955, inspired an enormous activity of algebraists worldwide. The activity culminated in two independent confirmations of the question in 1976 by Quillen and Suslin. In the meanwhile the algebraic K-theory was created, in which one ...

Endomorphism monoids have long been of interest in universal algebra and also in the study of particular classes of algebraic structures. For any algebra, the set of endomorphisms is closed under composition and forms a monoid (that is, a semigroup with identity). The endomorphism monoid is an interesting structure from a given algebra. In this thesis we study the structure and properties of th...

Motivated by results on the rationality of equivariant Hilbert series some hierarchical models in algebraic statistics we introduce Segre product formal languages and apply it to establish new cases. To this end show that two regular is again regular. We also prove every filtration algebras given as a tensor families with rational has series. The term used broadly include action monoid nonnegat...

It is shown that all nontrivial elements in higher K-groups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine toric varieties. 1. Statement of the main result The nilpotence conjecture in K-theory of toric varieties, treated in our previous works, asser...

The closure of a regular language under commutation or partial commutation has been extensively studied [1, 11, 12, 13], notably in connection with regular model checking [2, 3, 7] or in the study of Mazurkiewicz traces, one of the models of parallelism [14, 15, 16, 22]. We refer the reader to the survey [10, 9] or to the recent articles of Ochmański [17, 18, 19] for further references. In this...

In this paper, we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank [Formula: see text] all weak with vertices, which submonoid widely studied order-preserving transformations an text]-chain. Also, describe regular elements and calculate its size number idempotents.

Traces are a model for concurrency, whose formal definition is due to Mazurkiewicz [9]. In short, an alphabet A is fixed, with an independence relation on A. Traces can be defined as equivalence classes of words on A, under the relation that allows commutation of consecutive independent letters; and they are uniquely represented by certain A-labeled posets. A trace language is a set of traces o...