Value monoids of zero-dimensional valuations of rank 1

Value monoids of zero-dimensional valuations of rank 1

Classically, Gröbner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build on these ideas by providing a class of valuations on k(x, y) that are suitable for this framework. For these valuations, we compute ν(k[x, y]∗) and use this ...

Value Monoids of Zero-dimensional Valuations of Rank One

Classically, Gröbner bases are computed by first prescribing a fixed monomial order. Moss Sweedler suggested an alternative in the mid 1980s and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build on these ideas by providing a class of valuations on K(x, y) that are suitable for this framework. We then perform such computations for i...

Bieri-strebel Valuations (of Finite Rank)

Page Introduction 269 Notation and terminology 271 I. Basic facts 271 1. Review of IM 271 2. Review of AM 273 3. Solvable groups, aG, finite Priifer rank, FP 2 , and HNN-extensions . 276 4. Matrix computation of AM in the finite rank case . . . . 277 5. Finiteness conditions: F P m and finite presentation . . . . 278 6. The properties m-tameness and w-domestication 280 II. Proof that Hm{G, Y\ R...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

Affine Algebraic Monoids as Endomorphisms’ Monoids of Finite-dimensional Algebras

We prove that any affine algebraic monoid can be obtained as the endomorphisms’ monoid of a finite-dimensional (nonassociative) algebra.