Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-21T14:11:17Z No. of bitstreams: 1 arquivo total.pdf: 931330 bytes, checksum: 351b504f68153fb01d23f3fd1d96d2a0 (MD5) / Made available in DSpace on 2016-03-21T14:11:17Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 931330 bytes, checksum: 351b504f68153fb01d23f3fd1d96d2a0 (MD5) Previous issue date: 2013-04-29 / In this work, after the introduction of some concepts of Commutative Algebra, for instance dimension, minimal number of generators, and multiplicity, we prove the existence of a very special class of modules over Cohen-Macaulay rings, the so-called Ulrich modules. It is known that, if M is a maximal Cohen-Macaulay module over such ring, then (M) e(M). Our goal in this study is to prove the main cases where the equality (M) e(M) holds. / Neste trabalho, após introduzirmos alguns conceitos de Álgebra Comutativa, como dimensão, número mínimo de geradores, e multiplicidade, provamos a existência de uma classe de módulos bastante especial sobre anéis Cohen-Macaulay, os chamados módulos de Ulrich. É sabido que, se M é um A-módulo Cohen-Macaulay maximal sobre um tal anel, então (M) e(M). O objetivo do nosso estudo é demonstrar os principais casos em que vale (M) = e(M).

We compute the Hilbert-Kunz functions of two-dimensional rings of type ADE by using representations of their indecomposable, maximal Cohen-Macaulay modules in terms of matrix factorizations, and as first syzygy modules of homogeneous ideals.