associated prime ideal

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• Associated prime — In mathematics, an associated prime of a module M over a commutative ring R is a prime ideal of R that is the annihilator of some element of M . A module is called coprimary if xm = 0 for some nonzero m isin; M implies x n M = 0 for some positive …   Wikipedia

• Ideal sheaf — In algebraic geometry and other areas of mathematics, an ideal sheaf (or sheaf of ideals) is the global analogue of an ideal in a ring. The ideal sheaves on a geometric object are closely connected to its subspaces. Definition Let X be a… …   Wikipedia

• Radical of an ideal — In ring theory, a branch of mathematics, the radical of an ideal is a kind of completion of the ideal. There are several special radicals associated with the entire ring such as the nilradical and the Jacobson radical , which isolate certain bad… …   Wikipedia

• Eisenstein ideal — In mathematics, the Eisenstein ideal is a certain ideal in the endomorphism ring of the Jacobian variety of a modular curve. It was introduced by Barry Mazur in 1977, in studying the rational points of modular curves. The endomorphism ring in… …   Wikipedia

• Lasker–Noether theorem — In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be written as an intersection of finitely many primary ideals (which are related to, but not quite the same as, powers …   Wikipedia

• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

• Unique factorization domain — In mathematics, a unique factorization domain (UFD) is, roughly speaking, a commutative ring in which every element, with special exceptions, can be uniquely written as a product of prime elements, analogous to the fundamental theorem of… …   Wikipedia

• Valuation (algebra) — In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size… …   Wikipedia

• Proj construction — In algebraic geometry, Proj is a construction analogous to the spectrum of a ring construction of affine schemes, which produces objects with the typical properties of projective spaces and projective varieties. It is a fundamental tool in scheme …   Wikipedia

• Integral domain — In abstract algebra, an integral domain is a commutative ring that has no zero divisors,[1] and which is not the trivial ring {0}. It is usually assumed that commutative rings and integral domains have a multiplicative identity even though this… …   Wikipedia

• Chebotarev's density theorem — in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field Q of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic… …   Wikipedia