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Associated prime

In abstract algebra, an associated prime of a module M over a ring R is a type of prime ideal of R that arises as an annihilator of a (prime) submodule of M. The set of associated primes is usually denoted by Ass R ⁡ ( M ) , {\displaystyle \operatorname {Ass} _{R}(M),} and sometimes called the assassin or assassinator of M (word play between the notation…

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Associated prime

Nodes32
Edges31
Triples22
Avg. degree1.94
Density0.0625
Components1

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Associated prime

Top relations

related to Properties · 13
Associated prime → Any, Artinian, Ass, For, However, If, It, Lam, Matlis' Theorem, Moreover, Most, Noetherian, Spec
related to Definitions · 6
Associated prime → An, Ann, For, In, R-module, R/P
related to Examples · 2
Associated prime → If, The
is a · 1
Associated prime → annihilator

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Important terminology

associated displaystyle prime primes ring module ideal commutative ass noetherian submodule algebra set ideals mathrm called operatorname primary annihilator nonzero

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SubjectPredicateObjectConfidenceSrc
Associated primeis aannihilator0.90text
Associated primerelated to DefinitionsR-module0.60section
Associated primerelated to DefinitionsAnn0.60section
Associated primerelated to DefinitionsFor0.60section
Associated primerelated to DefinitionsAn0.60section
Associated primerelated to DefinitionsIn0.60section
Associated primerelated to DefinitionsR/P0.60section
Associated primerelated to ExamplesIf0.60section
Associated primerelated to ExamplesThe0.60section
Associated primerelated to PropertiesMost0.60section
Associated primerelated to PropertiesLam0.60section
Associated primerelated to PropertiesIf0.60section

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