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Generalization of Nilpotency of Ring Elements to Module Elements

Authors: David Ssevviiri; Nico Groenewald;

Generalization of Nilpotency of Ring Elements to Module Elements

Abstract

We define nilpotent and strongly nilpotent elements of a module M and show that the set 𝒩 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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
7
Top 10%
Top 10%
Average
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