THE LATTICE OF PRERADICALS OVER LOCAL UNISERIAL RINGS

摘要

In this paper we describe the lattice of preradicals over any local uniseriat ring (equiv-alently, any local artinian principal ideal ring). This lattice is isomorphic to a lattice of binary sequences of length n, where n is the length of the composition series for the ring, as a left and as a right module. We prove some of its properties: it is finite having cardinality 2n, it is distributive, self-dual and it is graded having rank n(n+1)/2 We also describe the correspondent posets of irreducible, join-irreducible, prime and coprime elements.