Module theory

Decomposition of a module

In abstract algebra, a decomposition of a module is a way to write a module as a direct sum of modules. A type of a decomposition is often used to define or characterize modules: for example, a semisimple module is a module that has a decomposition into simple modules. Given a ring, the types of decomposition of modules over the ring can also be used to define or characterize the ring: a ring is semisimple if and only if every module over it is a semisimple module. An indecomposable module is a module that is not a direct sum of two nonzero submodules. Azumaya's theorem states that if a module has an decomposition into modules with local endomorphism rings, then all decompositions into indecomposable modules are equivalent to each other; a special case of this, especially in group theory, is known as the Krull–Schmidt theorem. A special case of a decomposition of a module is a decomposition of a ring: for example, a ring is semisimple if and only if it is a direct sum (in fact a product) of matrix rings over division rings (this observation is known as the Artin–Wedderburn theorem). (Wikipedia).

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How to integrate by partial fractions

Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook How to integrate by the method of partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is a fraction such that the numerator

From playlist A second course in university calculus.

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Ex: Setting Up Partial Fraction Decomposition

This video provides several examples of how to set up the fractions in order to perform partial fraction decomposition. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Performing Partial Fraction Decomposition

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How to Set Up the Partial Fraction Decomposition

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Set Up the Partial Fraction Decomposition. Just setting them up. See my other videos for actual solved problems.

From playlist Partial Fraction Decomposition

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Ex 2: Partial Fraction Decomposition (Linear Factors)

This video explains how to perform partial fraction decomposition when the denominator has 2 distinct linear factors. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Performing Partial Fraction Decomposition

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Ex 1: Partial Fraction Decomposition (Linear Factors)

This video explains how to perform partial fraction decomposition when the denominator has 2 distinct linear factors. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Performing Partial Fraction Decomposition

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Partial Fraction Decomposition Part 1 (Linear)

This video introduces partial fraction decomposition.

From playlist Integration Using Partial Fractions

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Math 060 Linear Algebra 33 120514: Singular Value Decomposition 2/2

Singular Value Decomposition of a matrix: construction of the compact SVD; extending the matrices of the compact SVD to obtain the SVD.

From playlist Course 4: Linear Algebra

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(New Version Available) Partial Fraction Decomposition - Part 1 of 2

New Version Available: https://youtu.be/c2oLHtPA03U This video explain how to perform partial fraction decomposition with linear factors. http://mathispower4u.yolasite.com/

From playlist Integration Using Partial Fraction Decomposition

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Partial Fraction Decomposition - Part 2 of 2

This video explain how to perform partial fraction decomposition with linear and quadratic factors. http://mathispower4u.yolasite.com/

From playlist Integration Using Partial Fractions

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Steve Oudot (9/8/21): Signed barcodes for multi-parameter persistence via rank decompositions

In this talk I will introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally, of a poset representation. Like its unsigned counterpart in one-parameter persistence, the signed barcode

From playlist AATRN 2021

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Gregory Henselman-Petrusek (9/28/22): Saecular persistence

Homology with field coefficients has become a mainstay of modern TDA, thanks in part to structure theorems which decompose the corresponding persistence modules. This naturally begs the question -- what of integer coefficients? Or homotopy? We introduce saecular persistence, a categoric

From playlist AATRN 2022

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Hecke Endomorphism Algebras, Stratification, finite groups of Lie type, and ı-quantum algebras

Recorded for UVa Conference Presented by Jie Du (joint work with B. Marshall and L. Scott)

From playlist Pure seminars

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Francesco Vaccarino (8/29/21): Parallel decomposition of persistence modules through interval bases

We introduce an algorithm to decompose any finite-type persistence module with coefficients in a field into what we call an "interval basis". This construction yields both the standard persistence pairs of Topological Data Analysis (TDA), as well as a special set of generators inducing the

From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021

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Francesco Vaccarino (8/4/21): Parallel decomposition of persistence modules through interval bases

We introduce an algorithm to decompose any finite-type persistence module with coefficients in a field into what we call an "interval basis". This construction yields both the standard persistence pairs of Topological Data Analysis (TDA), as well as a special set of generators inducing the

From playlist AATRN 2021

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Stability and Periodicity in Modular Representation Theory - Nate Harman

Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Stability and Periodicity in Modular Representation Theory Speaker: Nate Harman Affiliation: Member, School of Mathematics Date: November 18, 2020 For more video please visit http://video.ias.edu

From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory

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Why do we care about characters of tilting modules? - Shotaro Makisumi

SL2 Seminar Topic: Why do we care about characters of tilting modules? Speaker: Shotaro Makisumi Affiliation: Columbia University; Member, School of Mathematics Date: January 26, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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Yonatan harpaz : The universal property of topological Hochschild homology

CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR

From playlist Topology

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Geordie Williamson, Lecture VI - 30 January 2015

Geordie Williamson (Max-Planck-Institute, Bonn) - Lecture VI http://www.crm.sns.it/course/4033/ This mini-course will be an introduction to perverse sheaves, with emphasis on examples from representation theory. It will be a course full of pictures and examples, with the aim of trying to

From playlist Lie Theory and Representation Theory - 2015

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Integration Using Partial Fraction Decomposition Part 1

This video shows how partial fraction decomposition can be used to simplify and integral. This video only shows linear factors. Part 1 of 2 Site: http://mathispower4u.com

From playlist Integration Using Partial Fractions

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Broué’s Abelian Defect Group Conjecture I - Jay Taylor

Seminar on Geometric and Modular Representation Theory Topic: Broué’s Abelian Defect Group Conjecture I Speaker: Jay Taylor Affiliation: University of Southern California; Member, School of Mathematics Date: September 9, 2020 For more video please visit http://video.ias.edu

From playlist Seminar on Geometric and Modular Representation Theory

Related pages

Converse (logic) | If and only if | Division ring | Krull–Schmidt theorem | Center (ring theory) | Ideal (ring theory) | Direct sum of modules | Semisimple module | Permutation | Countably generated module | Mathematical proof | Indecomposable module | Quotient module | Module homomorphism | Matrix ring | Free module | Minimal ideal | Unit (ring theory) | Integer | Simple module | Idempotent (ring theory) | Group theory | Mathematical induction | Ring (mathematics) | Endomorphism ring | Bijection | Characterization (mathematics) | Abstract algebra | Local ring | Kaplansky's theorem on projective modules | Matrix (mathematics) | Length of a module | Endomorphism | Image (mathematics) | Module (mathematics)