Math 101a: Algebra I Part B: Rings and Modules
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چکیده
In the unit on rings, I explained category theory and general rings at the same time. Then I talked mostly about commutative rings. In the unit on modules, I again mixed category theory into the basic notions and progressed to the structure theorem for finitely generated modules over PID’s. Jordan canonical forms were used as an application. The uniqueness part of the structure theorem was put off for the discussion on tensor product in Part C.
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Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module
Let be a local Cohen-Macaulay ring with infinite residue field, an Cohen - Macaulay module and an ideal of Consider and , respectively, the Rees Algebra and associated graded ring of , and denote by the analytic spread of Burch’s inequality says that and equality holds if is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of as In this paper we ...
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