We prove that left cancellative right hereditary monoids satisfying the dedekind height property are precisely the Zappa-Szép products of free monoids and groups. The ‘fundamental’ monoids of this type are in bijective correspondence with faithful self-similar group actions. 2000 AMS Subject Classification: 20M10, 20M50. 1 A class of left cancellative monoids This paper develops some ideas that...

Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...

0. Introduction. The literature on algebraic semigroups contains publications concerning two distinct types of semigroup extensions. Ideal extensions of semigroups were introduced by Clifford in [1] whereas Rédei [9] introduced Schreier extensions of monoids (a monoid is a semigroup containing an identity element). Let A and 5 be two disjoint semigroups and let 5" contain a zero element o. A se...

Let A be an algebra over a field K, m and n natural numbers P = (pji) fixed x matrix A. The K-vector space of all matrices the can made into with respect to following operation (o): B o C BPC. This is called Munn sandwich P. algebras such type arose as generalizations semigroup Rees semigroups which in turn are closely related simple semigroups. article describes generators defining relations M...

We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language – which is the number of its (left) quotients, and is the same as its state complexity – we also consider the size of its syntactic semigroup and the quotient complexity of its atoms – basic components of every...

Let X be an m × n matrix (m ≤ n) of indeterminates over a field K of positive characteristic, and denote the ideal generated by its t-minors by It . We show that the Rees ringR(It ) ofK[X], as well as the algebra At generated by the t-minors, are F-rational if charK > min(t, m − t). Without a restriction on characteristic this holds for K[X]/Ir+1 and the symbolic Rees ring R(It ). The determina...

Let $D$ be an integral domain and $\Gamma$ a torsion-free commutative cancellative (additive) semigroup with identity element quotient group $G$. In this paper, we show that if char$(D)=0$ (resp., char$(D)=p>0$), then $D[\Gamma]$ is weakly Krull only UMT-domain, UMT-monoid, $G$ of type $(0,0,0, \dots )$ except $p$). Moreover, give arithmetical applications result.

The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...

We determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of C-algebras for a large class of right LCM semigroups. The approach is based on abstract properties of the semigroup and covers the previous case studies on N⋊N, dilation matrices, self-similar actions, and Baumslag– Solitar monoids. At the same time, it provides new results for large clas...

In a recent paper, P.G. Trotter and the author introduced a \regular" semidirect product UV of e-varieties U and V. Among several speciic situations investigated there was the case V = RZ, the e-variety of right zero semigroups. Applying a covering theorem of McAlister, it was shown there that in several important cases (for instance for the e-variety of inverse semigroups), U RZ is precisely t...