The Hyperradical and The Hopkins-Levitzki Theorem for Modular Lattices

Details The Hyperradical and The Hopkins-Levitzki Theorem for Modular Lattices The Hyperradical and The Hopkins-Levitzki Theorem for Modular Lattices

2004-09-07

arxiv.org/abs/math/0409108v1

Mathematics

Rings and Algebras

7 pages, LaTeX

Scientific paper

Many arguments in the Theory of Rings and Modules are, on close inspection, purely Lattice theoretic arguments. Calagareanu} has a long repertoire of such results in his book. The Hopkins-Levitzki Theorem is interesting from this point of view, because a special case of it lends to an obvious lattice theory approach, but the rest is a little more subtle. Albu and Smith have obtained some sufficient conditions for the question of when Artinian implies Noetherian. Here we present a new approach, using the concept of Hyperradical; we obtain necessary and sufficient conditions.

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