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This subtopic studies representation theory of rings, about modules over algebras and the classification of their indecomposable and irreducible pieces.
16G10 studies representations of artinian rings in representation theory of rings. It studies how rings act on modules and how representation-theoretic invariants organize algebraic and combinatorial structure.
Representations of Artinian rings (Wikipedia)
Used to classify rings via their module categories and to analyze morphisms, sequences, and decomposition behavior.
16G20 studies representations of quivers and partially ordered sets in representation theory of rings. It studies how rings act on modules and how representation-theoretic invariants organize algebraic and combinatorial structure.
Representations of quivers and partially ordered sets (Wikipedia)
Used to classify rings via their module categories and to analyze morphisms, sequences, and decomposition behavior.
16G30 studies representations of orders, lattices, algebras over commutative rings in representation theory of rings. It studies how rings act on modules and how representation-theoretic invariants organize algebraic and combinatorial structure.
Representations of orders, lattices, algebras over commutative rings (Wikipedia)
Used to classify rings via their module categories and to analyze morphisms, sequences, and decomposition behavior.
16G50 studies cohen-macaulay modules in associative algebras in representation theory of rings. It studies how rings act on modules and how representation-theoretic invariants organize algebraic and combinatorial structure.
Cohen-Macaulay modules in associative algebras (Wikipedia)
Used to classify rings via their module categories and to analyze morphisms, sequences, and decomposition behavior.
16G60 studies representation type of associative algebras in representation theory of rings. It studies how rings act on modules and how representation-theoretic invariants organize algebraic and combinatorial structure.
Representation type of associative algebras (Wikipedia)
Used to classify rings via their module categories and to analyze morphisms, sequences, and decomposition behavior.
16G70 studies auslander-reiten sequences (almost split sequences) and related topics in representation theory of rings. It studies how rings act on modules and how representation-theoretic invariants organize algebraic and combinatorial structure.
Auslander-Reiten sequences (almost split sequences) and related topics (Wikipedia)
Used to classify rings via their module categories and to analyze morphisms, sequences, and decomposition behavior.