Generalization of Nilpotency of Ring Elements to Module Elements

We define nilpotent and strongly nilpotent elements of a module M and show that the set s (M) of all strongly nilpotent elements of M over a commutative unital ring R coincides with the classical prime radical β cl (M) the intersection of all classical prime submodules of M.

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Bibliographic Details
Published inCommunications in algebra Vol. 42; no. 2; pp. 571 - 577
Main Authors Ssevviiri, David, Groenewald, Nico
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.02.2014
Subjects
Algebra
Classical prime submodules
Nilpotent elements of modules
Strongly nilpotent elements of modules
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Summary:We define nilpotent and strongly nilpotent elements of a module M and show that the set s (M) of all strongly nilpotent elements of M over a commutative unital ring R coincides with the classical prime radical β cl (M) the intersection of all classical prime submodules of M.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2012.718822