algebraically closed field

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.

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  • 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

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  • 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

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