Radicals and $l$-modules

N. E. Shavgulidze

M. V. Lomonosov Moscow State University

Abstract: We show that for any special class of $l$-modules, we can define a special class of $l$-rings. We prove that the special radical of an $l$-ring $R$ can be represented as the intersection of the $l$-annihilators of $l$-modules over $R$ belonging to the special class. The prime radical of an $l$-ring $R$ can be represented as the intersection of the $l$-annihilators of $l$-prime $l$-modules over $R$.

UDC: 512.555.4+512.555.6

 English version: Journal of Mathematical Sciences (New York), 2010, 169:5, 717–723

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