On the left strongly prime modules and their radicals
Matematikos ir informatikos institutas |
| Date Issued |
|---|
2010 |
Charakterizuoti moduliai neturintys stipriai pirminių pomodulių. Baigtinai generuotiems moduliams virš žiedo surasta stipriai pirminio radikalo išraiška per polinominių modulių Džekobsono radikalus. Gauta stipriai pirminio vienpusio idealo išraiška per maksimaliuosius polinomų žiedų idealus.
We give the new results on the theory of the one-sided (left) strongly primemodules and their strongly prime radicals. Particularly, the conceptually new and shortproof of the A.L.Rosenberg’s theorem about one-sided strongly prime radical of the ring isgiven. Main results of the paper are: presentation of each left stongly prime idealpof aringRasp=R∩M, whereMis a maximal left ideal in a ring of polynomials over theringR; characterization of the primeless modules and characterization of the left stronglyprime radical of a finitely generated moduleMin terms of the Jacobson radicals of modulesof polynomesM〈X1, . . . , Xn〉