Value Monoids of Zero-dimensional Valuations of Rank One

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 ...

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

On Regularity of Acts

In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We als...

Realization of a certain class of semi-groups as value semi-groups of valuations

Given a well-ordered semi-group Γ with a minimal system of generators of ordinal type at most ωn 1 and of rational rank r, which satisfies a positivity and increasing condition, we construct a zero-dimensional valuation centered on the ring of polynomials with r variables such that the semigroup of the values of the polynomial ring is equal to Γ. The construction uses a generalization of Favre ...

Economic Valuation of the Shadegan Wetland

The Shadegan Wetland is located in the southwest of Iran. It is one of the wetlands internationally registered in the Ramsar Convention. Thanks to its variety of functionalities this wetlands has provided the local people with lots of job opportunities. Nowadays, as a result of located in the oil fields, this wetland is threatened by many of the projects run in its vicinity, like oil exploratio...