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 Title: Hypersurface Sections: A Study of Divisor Class Groups and of the Complexity of Tensor Products Author(s): Miller, Claudia Maria Doctoral Committee Chair(s): Griffith, P.A. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: The second part concerns the notion of complexity, a measure of the growth of the Betti numbers of a module. We show that over a complete intersection R the complexity of the tensor product $M\otimes\sb{R}N$ of two finitely generated modules is the sum of the complexities of each if $Tor\sbsp{i}{R}(M,\ N)=0$ for $i\ge1.$ One of the applications is simplification of the proofs of central results over hypersurface rings in a paper of C. Huneke and R. Wiegand on the tensor product of modules and the rigidity of Tor (HW1). Issue Date: 1997 Type: Text Language: English Description: 39 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997. URI: http://hdl.handle.net/2142/86953 Other Identifier(s): (MiAaPQ)AAI9812707 Date Available in IDEALS: 2015-09-28 Date Deposited: 1997
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