Field extensionIn mathematics, particularly in algebra, a field extension is a pair of fields such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers. Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry.
Minimal polynomial (field theory)In field theory, a branch of mathematics, the minimal polynomial of an element α of a field extension is, roughly speaking, the polynomial of lowest degree having coefficients in the field, such that α is a root of the polynomial. If the minimal polynomial of α exists, it is unique. The coefficient of the highest-degree term in the polynomial is required to be 1. More formally, a minimal polynomial is defined relative to a field extension E/F and an element of the extension field E/F.
LiquidationLiquidation is the process in accounting by which a company is brought to an end in Canada, United Kingdom, United States, Ireland, Australia, New Zealand, Italy, and many other countries. The assets and property of the company are redistributed. Liquidation is also sometimes referred to as winding-up or dissolution, although dissolution technically refers to the last stage of liquidation.
Administration (law)As a legal concept, administration is a procedure under the insolvency laws of a number of common law jurisdictions, similar to bankruptcy in the United States. It functions as a rescue mechanism for insolvent entities and allows them to carry on running their business. The process – in the United Kingdom colloquially called being "under administration" – is an alternative to liquidation or may be a precursor to it. Administration is commenced by an administration order.
