Spectrum (in algebraic geometry)

In algebraic geometry, the spectrum (denoted as Spec) of a ring is a fundamental construction that associates a geometric space to an algebraic object. Specifically, it is the set of all prime ideals of a commutative ring, equipped with a topology called the Zariski topology. This spectrum serves as a bridge between algebra and geometry, translating algebraic properties into geometric ones. Think of Spec as a “geometric space” representing solutions and structural features of polynomial equations encoded in the ring, providing a versatile framework to study shapes defined by algebraic equations systematically.