Abstract
With a simple graph G on [n], we associate a binomial ideal PG generated by diagonal minors of an n × n matrix X = (xij) of variables. We show that for any graph G, PG is a prime complete intersection ideal and determine the divisor class group of K[X]/PG. By using these ideals, one may find a normal domain with free divisor class group of any given rank.
ACKNOWLEDGMENT
The first author was supported by the grant UEFISCDI, PN-II-ID-PCE- 2011-3-1023.
Notes
Communicated by R. Wiegand.