Open AccessOn the left strongly prime modules and their radicals
Author(s) -
Algirdas Kaučikas
Publication year - 2010
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2011.05
Subject(s) - prime (order theory) , associated prime , radical , mathematics , ring (chemistry) , ideal (ethics) , characterization (materials science) , radical of an ideal , prime ideal , pure mathematics , discrete mathematics , combinatorics , principal ideal ring , chemistry , materials science , nanotechnology , commutative ring , law , commutative property , political science , organic chemistry
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) .