Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 3

Definition

Let $\struct {R, +, \circ}$ be a commutative and unitary ring.

A prime ideal of $R$ is a proper ideal $P$ of $R$ such that:

the complement $R \setminus P$ of $P$ in $R$ is closed under the ring product $\circ$.

Also see

• Equivalence of Definitions of Prime Ideal of Commutative and Unitary Ring

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $56$. Prime Ideal Topology
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $9$: Rings: Exercise $13$