On the left strongly prime modules and their radicals
Articles
Algirdas Kaučikas
Mykolas Romeris University
Published 2010-12-21
https://doi.org/10.15388/LMR.2011.05
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Keywords

strongly prime module
strongly prime ideal
primeless module
strongly prime radical
Jacobson radical

How to Cite

Kaučikas A. (2010) “On the left strongly prime modules and their radicals”, Lietuvos matematikos rinkinys, 51(proc. LMS), pp. 31–34. doi: 10.15388/LMR.2011.05.

Abstract

We give the new results on the theory of the one-sided (left) strongly prime modules and their strongly prime radicals. Particularly, the conceptually new and short proof of the A.L.Rosenberg’s theorem about one-sided strongly prime radical of the ring is given. Main results of the paper are: presentation of each left stongly prime ideal p of a ring R as p = R M, where M is a maximal left ideal in a ring of polynomials over the ring R; characterization of the primeless modules and characterization of the left strongly prime radical of a finitely generated module M in terms of the Jacobson radicals of modules of polynomes M(X1, . . . , Xni) .

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