English Dictionary

prime ring

noun

(algebra, ring theory) Any nonzero ring R such that for any two (two-sided) ideals P and Q in R, the product PQ = 0 (the zero ideal) if and only if P = 0 or Q = 0.

A prime ring is a ring in which the only two-sided ideals are the zero ideal and the ring itself.

意味（1）

(algebra, ring theory) Any nonzero ring R such that for any two (two-sided) ideals P and Q in R, the product PQ = 0 (the zero ideal) if and only if P = 0 or Q = 0.

A ring is called a prime ring if the product of nonzero ideals in it remains nonzero. It is obvious that a prime ring is necessarily semi-prime.