- algebraically closed field
*Math.*a field in which every polynomial equation with coefficients that are elements of the field has at least one root in the field, as the field of complex numbers.

*Useful english dictionary.
2012.*

- algebraically closed field
*Math.*a field in which every polynomial equation with coefficients that are elements of the field has at least one root in the field, as the field of complex numbers.

*Useful english dictionary.
2012.*

**Algebraically closed field**— In mathematics, a field F is said to be algebraically closed if every polynomial in one variable of degree at least 1, with coefficients in F , has a root in F . ExamplesAs an example, the field of real numbers is not algebraically closed,… … Wikipedia**algebraically closed field**— Math. a field in which every polynomial equation with coefficients that are elements of the field has at least one root in the field, as the field of complex numbers. * * * … Universalium**Quasi-algebraically closed field**— In mathematics, a field F is called quasi algebraically closed (or C1) if for every non constant homogeneous polynomial P over F has a non trivial zero provided the number of its variables is more than its degree. In other words, if P is a non… … 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**Real closed field**— In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… … Wikipedia**algebraically closed**— adjective Containing all roots of single variable polynomials in its elements. According to the fundamental theorem of algebra, the field of complex numbers is algebraically closed … Wiktionary**Differentially closed field**— In mathematics, a differential field K is differentially closed if every finite system of differential equations with a solution in some differential field extending K already has a solution in K. This concept was introduced by Robinson (1959).… … Wikipedia**Field arithmetic**— In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a ql|field (mathematics)|field and its absolute Galois group.It is an interdisciplinary subject as it uses tools from algebraic number… … 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**Glossary of field theory**— Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring… … Wikipedia