Commutative algebra | Ring theory
In abstract algebra, an Artinian ideal, named after Emil Artin, is encountered in ring theory, in particular, with polynomial rings. Given a polynomial ring R = k[X1, ... Xn] where k is some field, an Artinian ideal is an ideal I in R for which the Krull dimension of the quotient ring R/I is 0. Also, less precisely, one can think of an Artinian ideal as one that has at least each indeterminate in R raised to a power greater than 0 as a generator. If an ideal is not Artinian, one can take the Artinian closure of it as follows. First, take the least common multiple of the generators of the ideal. Second, add to the generating set of the ideal each indeterminate of the LCM with its power increased by 1 if the power is not 0 to begin with. An example is below. (Wikipedia).
Chris Stewart (Pt. 1) - Aesthetic Cognitivism: Overview & Concepts
Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all
From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series
Commutative algebra 25 Artinian rings
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 show that Artinian rings are Noetherian, probably the trickiest result of the course. As an application we
From playlist Commutative algebra
Commutative algebra 24 Artinian modules
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 define Artinian rings and modules, and give several examples of them. We then study finite length modules, show that they
From playlist Commutative algebra
Commutative algebra 26 (Examples of Artinian rings)
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 give some examples or Artin rings and write them as products of local rings. The examples include some Arti
From playlist Commutative algebra
Pascal Boyer - Aesthetic Cognitivism: Overview & Concepts
Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all
From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series
Teach Astronomy - Revolutions in Science and the Arts
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From playlist 03. Concepts and History of Astronomy and Physics
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From playlist WESTERN PHILOSOPHY
The Problem With Perfectionism
We aim for perfection without a correct idea of what perfection might demand from us. To strengthen our resolve, we need to improve our picture of what sacrifices any achievement will demand. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/p8kdj3 Join ou
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Christopher R. Brewer (Pt. 1) - Aesthetic Cognitivism I: Overview and Concepts
Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all
From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series
Friedrich Nietzsche was one of the great theorists of envy: he believed that envy is everywhere and that most of us don't even realise how much we feel it and the way it powers our behaviour. Having a good relationship with our envious tendencies was for Nietzsche a mark of maturity and wi
From playlist WESTERN PHILOSOPHY
A few introductory clips about Hegel's thought. #Philosophy #Hegel
From playlist Hegel
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From playlist Art Seeking Understanding - Closer To Truth - Core Topic
Thomas Zink - Grothendieck-Messing deformation theory for Hyper-Kähler manifolds
This is joint work with Andreas Langer. Let 𝑅 be an artinian local ring with perfect residue class field 𝑘. We define Hyper-Kähler manifolds 𝑋 and their Beauville-Bogomolov form over 𝑅. We give a lifting criterion in the spirit of Grothendieck and Messing. Over the small Witt ring 𝑊̂ (𝑅) w
From playlist Journées de géométrie arithmétique de l'IHÉS
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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From playlist Chalkless: Math PhD Updates
Commutative algebra 34 Geometry of normalizations
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 discuss the geometric meaning of finite morphisms and normal rings. Finite morphisms have the property that in the map of
From playlist Commutative algebra
Integrality of the Betti Moduli Space - Johan De Jong
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From playlist Mathematics
In this video I will show you some of my math books. I hope you enjoy this video. Calculus by Spivak https://amzn.to/3Dqr04n Everyday Calculus https://amzn.to/3TXpnSR Sets, Sequences, and Mappings https://amzn.to/3DmoSL4 Abstract Algebra by Dummit and Foote https://amzn.to/3Fy0x7R A First
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cohomology of GL(N), adjoint Selmer groups and simplicial deformation rings by Jacques Tilouine
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From playlist Perfectoid Spaces 2019