O. Horbachuk, Yu. Maturin, “On <nobr>$I$</nobr>-radicals”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, Number 2,Pages <nobr>89

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Research articles

On $I$-radicals

O. Horbachuk^a, Yu. Maturin^b

^a Department of Mechanics and Mathematics, Lviv National University, Lviv, Ukraine
^b Department of Mathematics, Institute of Physics, Mathematics and Computer Sciences, Drohobych State Pedagogical University, Drohobych, Lvivska Oblast, Ukraine

Abstract: In this paper $I$-radicals are studied. Rings are characterized with the help of $I$-radicals. For example, each $I$-radical over a left perfect ring splits if and only if this ring is a direct sum of finitely many left perfect rings, the Jacobson radicals of which are maximal ideals of them.

Keywords and phrases: Radical, $T$-nilpotent ideal, perfect ring.

MSC: 16D90

Received: 07.10.2004

Language: English