Radical of an ideal information

a branch of mathematics, the radical of an ideal I {\displaystyle I} of a commutative ring is another ideal defined by the property that an element x...

the radical symbol, radical sign, root symbol, radix, or surd is a symbol for the square root or higher-order root of a number. The square root of a number...

of an ideal, an important concept in abstract algebra Radical of a ring, an ideal of "bad" elements of a ring Jacobson radical, consisting of those elements...

mathematics, more specifically ring theory, the Jacobson radical of a ring R is the ideal consisting of those elements in R that annihilate all simple right...

theory, a branch of mathematics, a radical of a ring is an ideal of "not-good" elements of the ring. The first example of a radical was the nilradical...

In algebra, the real radical of an ideal I in a polynomial ring with real coefficients is the largest ideal containing I with the same (real) vanishing...

maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R...

over a field, then the radical of an ideal in A {\displaystyle A} is the intersection of all maximal ideals containing the ideal (because A {\displaystyle...

multiples of a given prime number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime. An ideal P of a...

ideal in it is maximal. The notion of a Goldman ideal can be used to give a slightly sharpened characterization of a radical of an ideal: the radical...

and this ideal is called the associated prime ideal of Q. In this situation, Q is said to be P-primary. On the other hand, an ideal whose radical is prime...

ideal Principal ideal Ideal quotient Maximal ideal, minimal ideal Primitive ideal, prime ideal, semiprime ideal Radical of an ideal Jacobson radical Socle...

(ACC) and descending chain condition (DCC) Fractional ideal Ideal class group Radical of an ideal Hilbert's Nullstellensatz Flat module Flat map Flat map...

I(V(J))={\sqrt {J}}.} Radical ideals (ideals that are their own radical) of k[V] correspond to algebraic subsets of V. Indeed, for radical ideals I and J, I ⊆...

generalization of a commutative ring Divisibility (ring theory): nilpotent element, (ex. dual numbers) Ideals and modules: Radical of an ideal, Morita equivalence...

ideal is an ideal consisting of nilpotent elements. 2.  The (Baer) upper nil radical is the sum of all nil ideals. 3.  The (Baer) lower nil radical is...

the radical of an ideal, the ideal of zero-dimensional schemes, Poincaré series and Hilbert functions, factorization of polynomials, and toric ideals. The...

non-zero abelian ideals; g {\displaystyle {\mathfrak {g}}} has no non-zero solvable ideals; the radical (maximal solvable ideal) of g {\displaystyle {\mathfrak...

ring is the set of all nilpotent elements in the ring, or equivalently the radical of the zero ideal. This is an ideal because the sum of any two nilpotent...

In mathematics, more specifically ring theory, an ideal I of a ring R is said to be a nilpotent ideal if there exists a natural number k such that I k...

generally, a homogeneous ideal of a graded ring is called an irrelevant ideal if its radical contains the irrelevant ideal. The terminology arises from...

(a·r)n = an·r n = 0, and by the binomial theorem, (a+b)m+n = 0. Therefore, the set of all nilpotent elements forms an ideal known as the nil radical of a ring...

denotes the taking of the variety defined by an ideal. If I is not radical, then the same property holds if we saturate the ideal J: Z ( I : J ∞ ) = c...

  A radical of an element x of a ring is an element such that some positive power is x. 4.  The radical of an ideal is the ideal of radicals of its elements...