quotient field
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Quotient ring — In mathematics a quotient ring, also known as factor ring or residue class ring, is a construction in ring theory, quite similar to the factor groups of group theory and the quotient spaces of linear algebra. One starts with a ring R and a two… … 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 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 emission — (FE) is the emission of electrons from the surface of a condensed phase into another phase due to the presence of high electric fields. In this phenomenon, electrons with energies below the Fermi level tunnel through the potential barrier at the… … 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
Quotient space (linear algebra) — In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by collapsing N to zero. The space obtained is called a quotient space and is denoted V / N (read V mod N ). Definition Formally, the construction is… … Wikipedia
Field of values — In matrix theory, the field of values associated with a matrix is the image of the unit sphere under the quadratic form induced by the matrix. More precisely, suppose A is a square matrix with complex entries. The field of values for A is the set … 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
Pseudo algebraically closed field — In mathematics, a field K is pseudo algebraically closed (usually abbreviated by PAC) if one of the following equivalent conditions holds:*Each absolutely irreducible variety V defined over K has a K rational point. *Each absolutely irreducible… … Wikipedia
Splitting field — In abstract algebra, a splitting field of a polynomial with coefficients in a field is a smallest field extension of that field over which the polynomial factors (or splits , hence the name) into linear factors. Contents 1 Definition 2 Facts 3 … Wikipedia
Intelligence quotient — IQ redirects here. For other uses, see IQ (disambiguation). Intelligence quotient Diagnostics An example of one kind of IQ test item, modeled after items in the Raven s Progressive Matrices test … Wikipedia
