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- Singular_submodule abstract "In the branches of abstract algebra known as ring theory and module theory, each right (resp. left) R module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left) ideals in R. In set notation it is usually denoted as . For general rings, is a good generalization of the torsion submodule t(M) which is most often defined for domains. In the case that R is a commutative domain, .If R is any ring, is defined considering R as a right module, and in this case is a twosided ideal of R called the right singular ideal of R. Similarly the left handed analogue is defined. It is possible for .This article will develop several notions in terms of the singular submodule and singular ideals, including the definition of singular module, nonsingular module and right and left nonsingular ring.".
- Singular_submodule wikiPageID "32191263".
- Singular_submodule wikiPageRevisionID "457820212".
- Singular_submodule hasPhotoCollection Singular_submodule.
- Singular_submodule subject Category:Abstract_algebra.
- Singular_submodule subject Category:Module_theory.
- Singular_submodule subject Category:Ring_theory.
- Singular_submodule comment "In the branches of abstract algebra known as ring theory and module theory, each right (resp. left) R module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left) ideals in R. In set notation it is usually denoted as . For general rings, is a good generalization of the torsion submodule t(M) which is most often defined for domains.".
- Singular_submodule label "Singular submodule".
- Singular_submodule sameAs m.0gy04qj.
- Singular_submodule sameAs Q7524251.
- Singular_submodule sameAs Q7524251.
- Singular_submodule wasDerivedFrom Singular_submodule?oldid=457820212.
- Singular_submodule isPrimaryTopicOf Singular_submodule.