GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES

Year 2008, Volume: 4 Issue: 4, 159 - 176, 01.12.2008

R. L. Mccasland P. F. Smith

Abstract

A challenging problem in recent years has been to find a good description of the radical of a submodule N of a (Noetherian) module M over a commutative ring, where the radical of N is the intersection of all prime submodules of M which contain N. In this paper we give a description of the radical of N in a Noetherian module M which is amenable to computation either by hand in simple cases or by using a computer algebra system in other cases, and illustrate this by examples.

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• School of Informatics University of Edinburgh Edinburgh EH8 9LE, Scotland UK e-mail: [e-mail] P.F. Smith Department of Mathematics University of Glasgow Glasgow G12 8QW, Scotland UK e-mail: [e-mail]