Math 603: Introduction to Commutative Algebra
نویسنده
چکیده
1.1. What is this course about? The foundations of differential geometry (= study of manifolds) rely on analysis in several variables as “local machinery”: many global theorems about manifolds are reduced down to statements about what happens in a local neighborhood, and then anaylsis is brought in to solve the local problem. Analogously, algebraic geometry uses commutative algebraic as its “local machinery”. Our goal is to study commutative algebra and some topics in algebraic geometry in a parallel manner. For a (somewhat) complete list of topics we plan to cover, see the course syllabus on the course web-page.
منابع مشابه
Commutative pseudo BE-algebras
The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...
متن کاملA Note on Perturbation Theory for Semi-groups of Operators
1. I. S. Cohen, Commutative rings with restricted minimum conditions, Duke Math. J. 17 (1950), 27-41. 2. S. MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771-782. 3. N. Nakano, Idealtheorie in einem speziellen unendlichen algebraischen Zahlkorper, J. Sei. Hiroshima Univ. 16(1953), 425-439. 4. O. Zariski and P. Samuel, Commutative a...
متن کاملFuzzy Filter Spectrum of a BCK Algebra
The notion of fuzzy s-prime filters of a bounded BCK-algebra is introduced.We discuss the relation between fuzzy s-prime filters and fuzzy prime filters. By the fuzzy s-prime filters of a bounded commutative BCK-algebra X, we establish a fuzzy topological structure on X. We prove that the set of all fuzzy s-prime filters of a bounded commutative BCK-algebra forms a topological space. Moreover, ...
متن کاملFinite - dimensional non - commutative Poisson algebras ]
Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. For finite-dimensional ones we show that if they are semisimple as associative algebras then they are standard, on the other hand, if they are semisimple as Lie algebras then their associative products are trivial. We also give the descriptions of ...
متن کاملSymplectic C ∞ -algebras
In this paper we show that a strongly homotopy commutative (or C∞-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-algebra (an ∞generalisation of a commutative Frobenius algebra introduced by Kontsevich). This result relies on the algebraic Hodge decomposition of the cyclic Hochschild cohomology of a C∞-algebra and does not generalize to al...
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