Spectrum of a ring

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 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]