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Everything about Semisimple module
Direct sum of irreducible modules
In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring that is a semisimple module over itself is known as an Artinian semisimple ring. Some important rings, such as group rings of finite groups over fields of characteristic zero, are semisimple rings. An Artinian ring is initially understood via its largest semisimple quotient. The structure of Artinian semisimple rings is well understood by the Artin–Wedderburn theorem, which exhibits these rings as finite direct products of matrix rings. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Semisimple moduleA 5-minute orientation
- Skim a recent paper: Permutation Module Decomposition of the Second Cohomology of a Regular Semisimple Hessenberg VarietyInfluential work since 2022
- Pick up a classic book: A filtered category OS and applicationsThe most-reprinted book on the subject
- Read the landmark paper: The Nichols algebra of a semisimple Yetter-Drinfeld moduleCited 81 times
- Go sideways: Noncommutative ringA closely related topic
- Go sideways: Glossary of ring theoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Nichols algebra of a semisimple Yetter-Drinfeld module
Module Categories Over Representations of SL q (2) in the Non-Semisimple Case
T-Semisimple Modules and T-Semisimple Rings
A key module over pure-semisimple hereditary rings
The cohomology of semisimple Lie algebras with coefficients in a Verma module
Finite semisimple module 2-categories
On the galois module structure of semisimple holomorphic differentials
On the endofiniteness of a key module over pure semisimple rings
🆕 Influential since 2022
Permutation Module Decomposition of the Second Cohomology of a Regular Semisimple Hessenberg Variety
Semisimple decompositions of Lie algebras and prehomogeneous modules
A specific intersection graph of a module applying semisimple property
The semisimple dimension of a certain type of module
Semisimple-continuous modules
📚 Books worth reading
A filtered category OS and applicationsRonald S. Irving · 1990
Categories of highest weight modulesThomas J. Enright · 1987
Stability in modules for classical lie algebrasGeorgia Benkart · 1990
Hodge theory, complex geometry, and representation theoryNSF/CBMS Regional Conference in the Mathematical Sciences: Hodge Theory, Complex Geometry, and Representation Theory (2012 Fort Worth, Tex.) · 2013- 📕Representation theory and mathematical physicsGregg Zuckerman · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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