location:  Publications → journals
Search results

Search: MSC category 14A05 ( Relevant commutative algebra [See also 13-XX] )

 Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2000 (vol 43 pp. 312)

Dobbs, David E.
 On the Prime Ideals in a Commutative Ring 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. Categories:13C15, 13B25, 04A10, 14A05, 13M05
 top of page | contact us | privacy | site map |