Noetherianity up to Symmetry - Jan Draisma
Members' Colloquium Topic: Noetherianity up to Symmetry Speaker: Jan Draisma Affiliation: Member, School of Mathematics Date: October 17, 2022 Noetherianity is a fundamental property of modules, rings, and topological spaces that underlies much of commutative algebra and algebraic geomet
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algebraic geometry 6 Noetherian spaces
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This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we find three equivalent ways of defining Noetherian rings, and give several examples of Noetherian and non-No
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This lecture is part of an online course on rings and modules. We define Noetherian rings, give several equivalent properties, and give some examples of rings that are or are not Noetherian. This will be continued in the next lecture about Hilbert's finiteness theorems. For the other
From playlist Rings and modules
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What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
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Schemes 15: Quasicompact, Noetherian
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This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we define Noetherian topological spaces, and use them to show that for a Noetherian ring R, every closed subse
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From playlist Fall 2017
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This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we define Noetherian modules over a ring, and use the to prove Noether's theorem that the agerba of invariants
From playlist Commutative algebra
Commutative algebra 36 Artin Rees lemma
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we state and prove the Artin-Rees lemma, which states that the restriction of an stable I-adic filtration (of
From playlist Commutative algebra
How do you determine if you have a linear equation
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Commutative algebra 58: System of parameters versus Krull
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We show that the smallest size of a system of parameters of a Noetherian local ring is at most the Krull dimension. The proof
From playlist Commutative algebra