JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 1, Pages 25 - 35
(April 2005)
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A BRIANÇN-SKODA THEOREM AND THE COHEN-MACAULAYNESS OF REES MODULES
Cornelia Naudé ¨South Africa)
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Abstract: Results on the Cohen-Macaulayness of a Rees ring and the associated graded ring are generalised to a Rees module R(I, N) and the associated graded module G(I, N) for N finitely generated module and I an ideal of definition of N. The tight closure of an ideal with respect to a module is defined and a relationship between the integral closure and the tight closure with respect to N is obtained. |
Keywords and phrases: Cohen-Macaulay, Rees modules, graded module, Brian篮-Skoda Theorem. |
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