multiplicative subset

English

Noun

multiplicative subset (plural multiplicative subsets)

1. (commutative algebra) A subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation.

   If $P$ is a proper prime ideal of a ring and $M$ is the set complement, w.r.t. the ring, of $P$, then $M$ is a multiplicative subset.