J Austral Math Soc Ser A 59 pp184--192, 1995.

On a Class of Radicals of Rings

R. Mazurek

Abstract

Let l be a property that a lattice of submodules of a module may possess and which is preserved under taking sublattices and isomorphic images of such lattices and is satisfied by the lattice of subgroups of the group of integer numbers. For a ring R the lower radical L generated by the class l(R) of R-modules whose lattice of submodules possesses the property l is considered. This radical determines the unique ideal L (R) of R, called the l-radical of R. We show that L is a Hoenke radical of rings. Although generally L is not a Kurosh-Amitsur radical, it has the ADS-property and the class of L-radical rings is closed under extensions. We prove that L (M_n(R)) Í M_n(L (R)) and give some illustrative examples.

1991 AMS Subject Classification: primary 16N99, 16S60; secondary 16S50

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Authors

R. Mazurek

Institute of Mathematics, University of Warsaw, Bialystok Division, Akademicka 2, 15-267 Bialystok, Poland.

mailto:mazurek@cksr.ac.bialystok.pl