Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 36 (1995), No. 1
A Note on Unions of Ideals and Cosets of Ideals
Michael Zandt
The paper gives a refinement to a well known and easy-to-prove
result of basic ideal theory: If an ideal $I$ is contained
in the union of a given finite collection of ideals, with at most
two of them not prime, $I$ must be contained in one of them. The
proposition, stated in this way,
leaves out the special structure of the ring under consideration. We show
that the lower bound implicit in the proposition can be replaced by the
minimum over cardinalities of residue fields of the given ring.
MSC 1991: 13A15