Monomial_Algebras

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title: Monomial Algebras permalink: wiki/Monomial_Algebras/ layout: wiki

Overview

Consider a semigroup A in NN^m and a subsemigroup B in A such that K[A] is finite over K[B].

We decompose the corresponding monomial algebra K[A] as a direct sum of ideals in K[B].

In Hoa and Stueckrad it is shown that this decomposition exists in the case that K[B] is isomorphic to a polynomial ring and is the Noether normalization of K[A] (the simplicial case). It is easy to see that the same is true in the general case.

The goal is to provide a Macaulay2 package for computing the decomposition.

To Do List

• Curve case
• Simplicial homogeneous case
• General case

Remarks

The package has moved to the Macaulay2 trunk.

References

Le Tuan Hoa, Juergen Stueckrad: Castelnuovo-Mumford regularity of simplicial toric rings, Journal of Algebra, Volume 259, Issue 1, 1 January 2003, Pages 127-146.

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