Groups can be studied using methods from diierent elds such as combina-torial group theory or string rewriting. Recently techniques from Grr obner basis theory for free monoid rings (non-commutative polynomial rings) respectively free group rings have been added to the set of methods due to the fact that monoid and group presentations (in terms of string rewriting systems) can be linked to spec...

We study the interaction between various analytification functors, and a class of morphisms rings, called homotopy epimorphisms. An functor assigns to simplicial commutative algebra over ring $R$, along with choice Banach structure on monoid in monoidal model category ind-Banach $R$-modules. show that several analytifications relevant analytic geometry - such as Tate, overconvergent, Stein anal...

For any free partially commutative monoid M(E, I), we compute the global dimension of the category of M(E, I)-objects in an Abelian category with exact coproducts. As a corollary, we generalize Hilbert’s Syzygy Theorem to polynomial rings in partially commuting variables.

Following Buchberger's approach to computing a Grr obner basis of a polynomial ideal in polynomial rings, a completion procedure for nitely generated right ideals in ZH] is given, where H is an ordered monoid presented by a nite, convergent semi{Thue system ((; T). Taking a nite set F ZH] we get a (possibly innnite) basis of the right ideal generated by F , such that using this basis we have un...

We combine the language of monoids with preorders so as to refine some fundamental aspects classical theory factorization and prove an abstract theorem a variety applications. In particular, we obtain generalization, from cancellative Dedekind-finite (commutative or non-commutative) monoids, on "atomic factorizations" that traces back work P.M. Cohn in 1960s; recover D.D. Anderson S. Valdes-Leo...

In this note we show that the nilpotence conjecture for toric varieties is true over any regular coefficient ring containing Q. In [G] we showed that for any additive submonoid M of a rational vector space with the trivial group of units and a field k with chark = 0 the multiplicative monoid N acts nilpotently on the quotient Ki(k[M ])/Ki(k) of the ith K-groups, i ≥ 0. In other words, for any s...