The Rees algebra of an ideal may be seen as a coordinate ring of a projective variety and it plays an important role in the study of algebraic singularities. Many parts of this theory can also be extended to the case of filtrations ideals or modules, as well to the case of the multi-Rees rings, which correspond to the case where the module is a direct sum of ideals. The definition of the Rees algebra of a module goes back to A. Micali, 1964 in the framework of his study of the general properties of the "universal algebras". More recently (2003), Simis-Ulrich-Vasconcelos devoted a entirely paper with 40 pages to the study of Rees algebras of modules, for their importance in algebraic geometry. In studying Rees algebras of modules and related concepts (reductions, integral closures...) one may attach to a module various ideals. In this talk we shall review some of these ideals and developed tools. This is based on a joint work with S. Zarzuela - University of Barcelona.
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