Spectrum of a ring

In commutative algebra, the prime spectrum (or simply the spectrum) of a commutative ring ${\displaystyle R}$ is the set of all prime ideals of ${\displaystyle R}$, and is usually denoted by ${\displaystyle \operatorname {Spec} {R}}$;^[1] in algebraic geometry it is simultaneously a topological space equipped with the sheaf of rings ${\displaystyle {\mathcal {O}}}$.^[2]