multiplicative subset

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