To a given type of algebraic systems # there corresponds at least one first order language L. One can then ask whether a property P, defined for members of #, is expressible in the language L. In other words, is there a set of sentences II such that a member M of # has property P if and only if all sentences in n are true in M. If the set II exists we say that P is definable in L. Further, Q) i...

Assume that G is a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain. Then G is torsion free. The result applies in particular to all finite Coxeter type Artin groups. Finding an elementary proof for the fact that Artin’s braid groups are torsion free has been reported to be a longstanding open question [9]. The exis...

In this paper, we introduce the notion of an orientation-preserving transformation on arbitrary chain, as a natural extension for infinite chains well known concept finite introduced in 1998 by McAlister and, independently, 1999 Catarino and Higgins. We consider monoid POP(X)(X) all partial transformations or chain X its submonoids POPI(X) full permutations X, respectively. The OPPO(X) order-pr...

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 prove that if $m$ is a monoid and $a$ a finite set with more than one element‎, ‎then the residual finiteness of $m$ is equivalent to that of the monoid consisting of all cellular automata over $m$ with alphabet $a$‎.

Let D be a domain and let S torsion-free monoid such that has characteristic 0 or the quotient group of satisfies ascending chain condition on cyclic subgroups. We give characterization when algebra [ ] is weakly Krull. As corollaries, we reobtain results Krull resp. factorial, due to Chouinard Chang. Furthermore, deduce generalized algebras analogous our main result characterize domains among ...

The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kau¤man. Borisavljevíc, Došen and Petríc gave a complete proof of its abstract presentation by generators and relations, and suggested the name ‘Kau¤man monoid’. We bring the theory of semigroups to the study of a certain …nite homomorphic image o...

We define and study the Picard group of a monoid scheme and the class group of a normal monoid scheme. To do so, we develop some ideal theory for (pointed abelian) noetherian monoids, including primary decomposition and discrete valuations. The normalization of a monoid turns out to be a monoid scheme, but not always a monoid.