Please note, due to essential maintenance online purchasing will be unavailable between 08:00 and 12:00 (BST) on 24th February 2019. We apologise for any inconvenience.
If n and m are positive integers, necessary and sufficient conditions are given for the existence of a finite commutative ring R with exactly n elements and exactly m prime ideals. Next, assuming the Axiom of Choice, it is proved that if R is a commutative ring and T is a commutative R-algebra which is generated by a set I, then each chain of prime ideals of T lying over the same prime ideal of R has at most 2|I| elements. A polynomial ring example shows that the preceding result is best-possible.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.