Nilpotent elements control the structure of a module

2018/12/11 by Ssevviiri, David
#16D60 #16D70 #16S90 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1812.04320

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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