field of fractions

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• Field of fractions — In mathematics, every integral domain can be embedded in a field; the smallest field which can be used is the field of fractions or field of quotients of the integral domain. The elements of the field of fractions of the integral domain R have… …   Wikipedia

• Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

• Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… …   Wikipedia

• field of quotients — Math. a field whose elements are pairs of elements of a given commutative integral domain such that the second element of each pair is not zero. The field of rational numbers is the field of quotients of the integral domain of integers. Also… …   Universalium

• field of quotients — Math. a field whose elements are pairs of elements of a given commutative integral domain such that the second element of each pair is not zero. The field of rational numbers is the field of quotients of the integral domain of integers. Also… …   Useful english dictionary

• Field desorption — [ mass spectrometer at right] Field desorption (FD)/field ionization (FI) refers to an ion source for mass spectrometry first reported by Beckey in 1969. [Beckey H.D. Field ionization mass spectrometry. Research/Development, 1969 , 20(11), 26] In …   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

• Function field of an algebraic variety — In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V . In complex algebraic geometry these are meromorphic functions and their higher dimensional analogues; in… …   Wikipedia

• Function field (scheme theory) — In algebraic geometry, the function field KX of a scheme X is a generalization of the notion of a sheaf of rational functions on a variety. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on …   Wikipedia

• Local field — In mathematics, a local field is a special type of field that is a locally compact topological field with respect to a non discrete topology.[1] Given such a field, an absolute value can be defined on it. There are two basic types of local field …   Wikipedia

• Global field — In mathematics, the term global field refers to either of the following:*a number field, i.e., a finite extension of Q or *the function field of an algebraic curve over a finite field, i.e., a finitely generated field of characteristic p >0 of… …   Wikipedia