Càlcul en anells locals

Abstract

[en] Local Rings are rings with a single maximal ideal. This report consists on the study of this type of rings and, following a parallel structure to the one used in the study of Multivariate Polynomial Rings, we arrive at the construction of standard bases. In order to define standard bases, we will have to study previous theorems and algorithms. Among the most important ones, we can find Mora’s algorithm. This algorithm will allow us to divide polynomials in Local Rings. Finally, we will apply the standard bases using a program called Singular.