Algebra

Smooth algebra

In algebra, a commutative k-algebra A is said to be 0-smooth if it satisfies the following lifting property: given a k-algebra C, an ideal N of C whose square is zero and a k-algebra map , there exists a k-algebra map such that u is v followed by the canonical map. If there exists at most one such lifting v, then A is said to be 0-unramified (or 0-neat). A is said to be 0-étale if it is 0-smooth and 0-unramified. The notion of 0-smoothness is also called formal smoothness. A finitely generated k-algebra A is 0-smooth over k if and only if Spec A is a smooth scheme over k. A separable algebraic field extension L of k is 0-étale over k. The formal power series ring is 0-smooth only when and (i.e., k has a finite p-basis.) (Wikipedia).

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Linear Transformations: Onto

Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.

From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

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Advanced Linear Algebra Full Video Course

Linear algebra is central to almost all areas of mathematics. For instance, #linearalgebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of

From playlist Linear Algebra

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11_3_7 A Smooth Function

Prerequisites of a smooth function.

From playlist Advanced Calculus / Multivariable Calculus

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Linear Algebra for Beginners | Linear algebra for machine learning

Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. In this course you will learn most of the basics of linear algebra wh

From playlist Linear Algebra

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12A Equations of a Plane

Using the general and vector forms of the equation of a plane from the normal and a point, or two points on the plane.

From playlist Linear Algebra

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Algebra for Beginners | Basics of Algebra

#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten

From playlist Linear Algebra

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11D The Norm of a Vector

The norm or length of a vector.

From playlist Linear Algebra

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10A An Introduction to Eigenvalues and Eigenvectors

A short description of eigenvalues and eigenvectors.

From playlist Linear Algebra

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Linear Transformations: One-One

Linear Algebra: We recall the definition of one-one for functions and apply it to linear transformations. We obtain a simple rule for checking one-one in this case: either the kernel is zero or the associated matrix has a pivot in each column in row echelon form. Several examples are gi

From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

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Akhil Mathew - Some recent advances in syntomic cohomology (3/3)

Bhatt-Morrow-Scholze have defined integral refinements $Z_p(i)$ of the syntomic cohomology of Fontaine-Messing and Kato. These objects arise as filtered Frobenius eigenspaces of absolute prismatic cohomology and should yield a theory of "p-adic étale motivic cohomology" -- for example, the

From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)

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Algebraic groups in positive characteristic - Srimathy Srinivasan

Short talks by postdoctoral members Topic: Algebraic groups in positive characteristic Speaker: Srimathy Srinivasan Affiliation: Member, School of Mathematics Date: October 4, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

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Erik van Erp: Lie groupoids in index theory 1

The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 9.9.2014

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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Oliver Gabriel: Functorial Rieffel deformations and (periodic) cyclic cohomology

Inspired by previous work by S. Brain, G. Landi and W. van Suijlekom, we study functorial deformations of algebras and modules based on actions of Abelian locally compact groups. We consider the case of G = S^1 \times \mathbb Z, provide an explicit form for the deformation and show how fun

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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Hodge Theory -- From Abel to Deligne - Phillip Griffiths

Phillip Griffiths School of Mathematics, Institute for Advanced Study October 14, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Erik van Erp: Lie groupoids in index theory 2

The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 9.9.2014

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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Paolo Piazza: Proper actions of Lie groups and numeric invariants of Dirac operators

HYBRID EVENT shall explain how to define and investigate primary and secondary invariants of G-invariant Dirac operators on a cocompact G-proper manifold, with G a connected real reductive Lie group. This involves cyclic cohomology and Ktheory. After treating the case of cyclic cocycles a

From playlist Lie Theory and Generalizations

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Olivier Benoist: Algebraic approximation of submanifolds of real algebraic varieties

CONFERENCE Recording during the thematic meeting : "Real Aspects of Geometry" the November 1, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audi

From playlist Algebraic and Complex Geometry

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Linear Algebra 2n: Spanning Sets

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

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M. Pflaum: Localization in Hochschild homology and convolution algebras of circle actions

Talk by Shintaro Nishikawa in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on July 29, 2020.

From playlist Global Noncommutative Geometry Seminar (Americas)

Related pages

Algebraic extension | Field extension | P-basis | Smooth scheme | Étale morphism | Local ring | Field (mathematics) | Popescu's theorem | Algebra over a field | Maximal ideal | Algebra | Regular ring | Ring (mathematics) | Separable extension