Applications of Modules in Representation Theory
A detailed guide to applications of modules in representation theory. Covers key methods, mathematical significance, and real-world applications.
Mathematics Category
Modules
51 articles
≈ 510 min total reading
Artinian Modules and Descending Chains
A detailed guide to artinian modules and descending chains. Covers key methods, mathematical significance, and real-world applications.
Associated Primes of Modules
A detailed guide to associated primes of modules. Covers key methods, mathematical significance, and real-world applications.
Categorical Approach to Module Theory
A detailed guide to categorical approach to module theory. Covers key methods, mathematical significance, and real-world applications.
Clifford Theory for Group Representations
A detailed guide to clifford theory for group representations. Covers key methods, mathematical significance, and real-world applications.
Cohomology of Module Complexes
A detailed guide to cohomology of module complexes. Covers key methods, mathematical significance, and real-world applications.
Completion of Modules at Ideals
A detailed guide to completion of modules at ideals. Covers key methods, mathematical significance, and real-world applications.
Composition Series and Jordan Holder
A detailed guide to composition series and jordan holder. Covers key methods, mathematical significance, and real-world applications.
Cotorsion Pairs in Module Theory
A detailed guide to cotorsion pairs in module theory. Covers key methods, mathematical significance, and real-world applications.
Definition of Modules Over a Ring
A detailed guide to definition of modules over a ring. Covers key methods, mathematical significance, and real-world applications.
Derived Functors of Module Theory
A detailed guide to derived functors of module theory. Covers key methods, mathematical significance, and real-world applications.
Direct Sums and Products of Modules
A detailed guide to direct sums and products of modules. Covers key methods, mathematical significance, and real-world applications.
Divisible Groups as Z-Modules
A detailed guide to divisible groups as z-modules. Covers key methods, mathematical significance, and real-world applications.
Exact Sequences of Module Homomorphisms
A detailed guide to exact sequences of module homomorphisms. Covers key methods, mathematical significance, and real-world applications.
Filtered Modules and Completeness
A detailed guide to filtered modules and completeness. Covers key methods, mathematical significance, and real-world applications.
Finitely Generated Modules Over PIDs
A detailed guide to finitely generated modules over pids. Covers key methods, mathematical significance, and real-world applications.
Fitting Invariants and Module Structure
A detailed guide to fitting invariants and module structure. Covers key methods, mathematical significance, and real-world applications.
Flat Modules and Tensor Products
A detailed guide to flat modules and tensor products. Covers key methods, mathematical significance, and real-world applications.
Free Modules and Their Bases
A detailed guide to free modules and their bases. Covers key methods, mathematical significance, and real-world applications.
Free Modules and Their Bases (Modules)
A detailed guide to free modules and their bases (modules). Covers key methods, mathematical significance, and real-world applications.
Frobenius Reciprocity in Module Context
A detailed guide to frobenius reciprocity in module context. Covers key methods, mathematical significance, and real-world applications.
Functors Between Module Categories
A detailed guide to functors between module categories. Covers key methods, mathematical significance, and real-world applications.
Gabriel-Popescu Theorem for Module Embedding
A detailed guide to gabriel-popescu theorem for module embedding. Covers key methods, mathematical significance, and real-world applications.
Gorenstein Projective Modules Defined
A detailed guide to gorenstein projective modules defined. Covers key methods, mathematical significance, and real-world applications.
Graded Modules and Graded Rings
A detailed guide to graded modules and graded rings. Covers key methods, mathematical significance, and real-world applications.
Hom and Tensor Adjunction for Modules
A detailed guide to hom and tensor adjunction for modules. Covers key methods, mathematical significance, and real-world applications.
Homological Dimensions of Modules
A detailed guide to homological dimensions of modules. Covers key methods, mathematical significance, and real-world applications.
Injective Modules and Extension Properties
A detailed guide to injective modules and extension properties. Covers key methods, mathematical significance, and real-world applications.
Integral Closure and Module Extensions
A detailed guide to integral closure and module extensions. Covers key methods, mathematical significance, and real-world applications.
Krull-Schmidt Theorem for Module Decomposition
A detailed guide to krull-schmidt theorem for module decomposition. Covers key methods, mathematical significance, and real-world applications.
Localization of Modules at Multiplicative Sets
A detailed guide to localization of modules at multiplicative sets. Covers key methods, mathematical significance, and real-world applications.
Module Homomorphisms and Endomorphisms
A detailed guide to module homomorphisms and endomorphisms. Covers key methods, mathematical significance, and real-world applications.
Module Structures in Computer Science
A detailed guide to module structures in computer science. Covers key methods, mathematical significance, and real-world applications.
Module Theory in Algebraic Geometry
A detailed guide to module theory in algebraic geometry. Covers key methods, mathematical significance, and real-world applications.
Modules in Cryptographic Protocol Design
A detailed guide to modules in cryptographic protocol design. Covers key methods, mathematical significance, and real-world applications.
Modules Over Endomorphism Rings of Modules
A detailed guide to modules over endomorphism rings of modules. Covers key methods, mathematical significance, and real-world applications.
Modules Over Noncommutative Rings
A detailed guide to modules over noncommutative rings. Covers key methods, mathematical significance, and real-world applications.
Modules Over Polynomial Rings
A detailed guide to modules over polynomial rings. Covers key methods, mathematical significance, and real-world applications.
Modules Over Principal Ideal Domains
A detailed guide to modules over principal ideal domains. Covers key methods, mathematical significance, and real-world applications.
Morita Equivalence of Module Categories
A detailed guide to morita equivalence of module categories. Covers key methods, mathematical significance, and real-world applications.
Noetherian Modules and Ascending Chains
A detailed guide to noetherian modules and ascending chains. Covers key methods, mathematical significance, and real-world applications.
Primary Decomposition of Modules
A detailed guide to primary decomposition of modules. Covers key methods, mathematical significance, and real-world applications.
Projective Modules and Lifting Properties
A detailed guide to projective modules and lifting properties. Covers key methods, mathematical significance, and real-world applications.
Simple Modules and Semisimple Modules
A detailed guide to simple modules and semisimple modules. Covers key methods, mathematical significance, and real-world applications.
Stable Module Categories and Syzygies
A detailed guide to stable module categories and syzygies. Covers key methods, mathematical significance, and real-world applications.
Submodules and Quotient Modules
A detailed guide to submodules and quotient modules. Covers key methods, mathematical significance, and real-world applications.
Syzygies and Free Resolutions
A detailed guide to syzygies and free resolutions. Covers key methods, mathematical significance, and real-world applications.
Tensor Product of Two Modules
A detailed guide to tensor product of two modules. Covers key methods, mathematical significance, and real-world applications.
Torsion Modules and Torsion Submodules
A detailed guide to torsion modules and torsion submodules. Covers key methods, mathematical significance, and real-world applications.
Torsion Theories and Module Localization
A detailed guide to torsion theories and module localization. Covers key methods, mathematical significance, and real-world applications.
Torsion-Free Modules Over Integral Domains
A detailed guide to torsion-free modules over integral domains. Covers key methods, mathematical significance, and real-world applications.