Factorizations of free monoids and unavoidable regularities

Transitive factorizations of free partially commutative monoids and Lie algebras

Let M(A, θ) be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet B ⊂ A such that the right factor of a bisection M(A, θ) = M(B, θB).T be also partially commutative free. This extends strictly the (classical) elimination theory on partial commutations and allows to construct new factorizations of M(A, θ) and associated bases of LK(A, θ).

Factorizations of Algebraic Integers, Block Monoids, and Additive Number Theory

Let D be the ring of integers in a finite extension of the rationals. The classic examination of the factorization properties of algebraic integers usually begins with the study of norms. In this paper, we show using the ideal class group, C(D), of D that a deeper examination of such properties is possible. Using the class group, we construct an object known as a block monoid, which allows us t...

-torsion free Acts Over Monoids

In this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. Then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right Rees factor, cyclic and acts in general  implies some other properties, respectively.

Free Factorizations

-torsion free acts over monoids

in this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right rees factor, cyclic and acts in general  implies some other properties, respectively.