algebra, the prime spectrum (or simply the spectrum) of a commutative ring R {\displaystyle R} is the set of all prime ideals of R {\displaystyle R}...

theory, a ring spectrum is a spectrum E together with a multiplication map μ: E ∧ E → E and a unit map η: S → E, where S is the sphere spectrum. These...

later generalized for making the set of prime ideals of a commutative ring (called the spectrum of the ring) a topological space. The Zariski topology...

spectrum  is also naturally a topological space; this is similar to the notion of the spectrum of a ring. One of the most important applications of this...

the formal spectrum of A, denoted Spf A. Spf A has a structure sheaf which is defined using the structure sheaf of the spectrum of a ring. Let J λ {\displaystyle...

different parts of the sexuality spectrum. A white ring may be worn on one's left middle finger to indicate one's identity on the aromantic spectrum. This was...

Global Spectrum may refer to: Comcast Spectacor Spectrum of a ring#Global or relative Spec This disambiguation page lists articles associated with the...

of the prime ideals of any commutative ring; for this topology, the closed sets are the sets of prime ideals that contain a given ideal. The spectrum...

inverted. A combination of two different lights of the emotional spectrum can neutralize black rings, rendering them vulnerable. Once a black ring is destroyed...

a commutative ring spectrum, roughly equivalent to a E ∞ {\displaystyle E_{\infty }} -ring spectrum, is a commutative monoid in a good category of spectra...

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...

the solution sets of systems of polynomial equations. Spectral: A space is spectral if and only if it is the prime spectrum of a ring (Hochster theorem)...

S-phase-promoting factor, in biology Formal spectrum of a ring, a construction in algebraic geometry Spray polyurethane foam, a building insulation material Spruce-pine-fir...

localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/module...

definition of the spectrum of a ring Spec(R), the space of prime ideals of R equipped with the Zariski topology, that the Krull dimension of R is equal...

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

mathematics, a highly structured ring spectrum or A ∞ {\displaystyle A_{\infty }} -ring is an object in homotopy theory encoding a refinement of a multiplicative...

In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is...

primitive rings are all fields. The primitive spectrum of a ring is a non-commutative analog of the prime spectrum of a commutative ring. Let A be a ring and...

Proj is a construction analogous to the spectrum-of-a-ring construction of affine schemes, which produces objects with the typical properties of projective...

form a continuum. Spectrum may also refer to: Electromagnetic spectrum Visible spectrum or optical spectrum, a subset of the electromagnetic spectrum Emission...

{\displaystyle \mathrm {Spec} (R)} (cf. spectrum of a ring) for which the generic fibre constructed by means of the morphism S p e c ( F ) → S p e c (...

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

coefficient ring of X {\displaystyle X} when X {\displaystyle X} is a ring spectrum. X ∧ Y {\displaystyle X\land Y} is the smash product of two spectra...

{Z} }}} , then a sheaf of O-modules is the same as a sheaf of abelian groups (i.e., an abelian sheaf). If X is the prime spectrum of a ring R, then any R-module...

on an algebraic variety or on the spectrum of a ring, used in algebraic geometry, the topological vector space of all functions from the real line R...

the spectrum of a ring, which is used in algebraic geometry. A non-normal space of some relevance to analysis is the topological vector space of all functions...

Lasker–Noether theorem Noether normalization lemma Going up and going down Spectrum of a ring Zariski tangent space Kähler differential Elimination theory Gröbner...

(that is, the prime spectrum of a ring) is T0 but not, in general, T1. To see this, note that the closure of a one-point set is the set of all prime ideals...

terminology of geometric Frobenius arises by applying the spectrum of a ring construction to φ. This gives a mapping φ*: Spec(Rp) → Spec(R) of affine schemes...