In abstract algebra, a nonzero ring R is a prime ring if for any two elements a and b of R, arb = 0 for all r in R implies that either a = 0 or b = 0....

In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the...

than to the elements of the ring. For instance, the prime ideals of a ring are analogous to prime numbers, and the Chinese remainder theorem can be generalized...

In commutative algebra, the prime spectrum (or simply the spectrum) of a commutative ring R is the set of all prime ideals of R, and is usually denoted...

Rings: The Rings of Power is an American fantasy television series developed by J. D. Payne and Patrick McKay for the streaming service Amazon Prime Video...

with ring elements. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal...

residue class ring modulo a Gaussian integer z0 is a field if and only if z 0 {\displaystyle z_{0}} is a Gaussian prime. If z0 is a decomposed prime or the ramified...

of a ring Simplicial commutative ring Special types of rings: Boolean ring Dedekind ring Differential ring Exponential ring Finite ring Lie ring Local...

mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra...

subset of a Boolean ring is a ring ideal (prime ring ideal, maximal ring ideal) if and only if it is an order ideal (prime order ideal, maximal order ideal)...