Short notes

Radicals of $l$-rings and special classes of $l$-modules

N. E. Shavgulidze

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A special class of lattice-ordered modules is studied. We show that for any special class of $l$-modules we can define a special class of $l$-rings. 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 $R$.

Key words: lattice-ordered ring, lattice-ordered module, special class of $l$-modules, special radical of an $l$-ring, prime radical of an $l$-ring.

UDC: 512.555.4

Received: 27.05.2009

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