Length functions determined by killing powers of several ideals in a local ring

Commutative Algebra;Rings;Hilbert Functions;Hilbert-Kunz Functions;Intersection Multiplicities;Quasipolynomial Functions;Mathematics;Mathematics;Science;Mathematics

Fields, J. BruceSmith, Karen ;

University of Michigan

关键词: Commutative Algebra;    Rings;    Hilbert Functions;    Hilbert-Kunz Functions;    Intersection Multiplicities;    Quasipolynomial Functions;    Mathematics;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/57281/fields_thesis.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Given a local ring Rand n ideals whose sum is primary to the maximal ideal of R, one may define a function which takes an n-tuple of exponents to the length of the quotient of R by sum of the ideals raised to the respective exponents. This quotient can also be obtained by taking the tensor product of the quotients of Rby the various powers of the ideals. This thesis studies these functions as well as the functions obtained by replacing the tensor product by a higher Tor. These functions are shown to have rational generating functions under certain conditions.