We don't have synonyms for prime ring yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are prize ring, crime ring and price ring.
(n) :
(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.
(n) :
(algebra, ring theory) Synonym of prime subring.
(n) :
(algebra, ring theory, uncommon) A ring which is equal to its own prime subring.
(n) :
(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.
(n) :
(algebra, ring theory) Synonym of prime subring.
(n) :
(algebra, ring theory, uncommon) A ring which is equal to its own prime subring.