%0 Thesis %A Ulloa-Esquivel, Roberto Antonio %D 2020 %T Epsilon multiplicity of modules with Noetherian saturation algebras %U https://hammer.purdue.edu/articles/thesis/Epsilon_multiplicity_of_modules_with_Noetherian_saturation_algebras/12735638 %R 10.25394/PGS.12735638.v1 %2 https://hammer.purdue.edu/ndownloader/files/24106025 %K Commutative algebra %K Algebra %K Multiplicity theory %K epsilon multiplicity %K Pure Mathematics not elsewhere classified %X In the need of computational tools for epsilon-multiplicity, we provide a criterion for a module with a rank E inside a free module F to have rational epsilon-multiplicity in terms of the finite generation of the saturation Rees algebra of E. In this case, the multiplicity can be related to a Hilbert multiplicity of certain graded algebra. A particular example of this situation is provided: it is shown that the epsilon-multiplicity of monomial modules is Noetherian. Numerical evidence is provided that leads to a conjecture formula for the epsilon-multiplicity of certain monomial curves in the 3-affine space. %I Purdue University Graduate School