Group rings with n-generated ideals

Abstract

Let R be a commutative ring with identity. If an ideal I of R can be generated by n elements, then we say that I is n-generated; and, if every ideal of R is n-generated, we say that R has the n-generator property. It is well-known that if R has the n-generator property, then R has Krull dimension zero or one. Considerable interest has been shown in rings with the n-generator property (see for example [4], [13], [17], [la]) and in the problem of determining when a group or monoid ring has the n-generator property - either in general or for a specified choice of n, see [I], [lo], [ll], [14] and [19].