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arXiv · 1812.04320

Nilpotent elements control the structure of a module

David Ssevviiri
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Abstract

A relationship between nilpotency and primeness in a module is investigated. Reduced modules are expressed as sums of prime modules. It is shown that presence of nilpotent module elements inhibits a module from possessing good structural properties. A general form is given of an example used in literature to distinguish: 1) completely prime modules from prime modules, 2) classical prime modules from classical completely prime modules, and 3) a module which satisfies the complete radical formula from one which is neither 2-primal nor satisfies the radical formula.

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David Ssevviiri. 2018-12-11. Nilpotent elements control the structure of a module. https://arxiv.org/abs/1812.04320

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