Degree of a field extensionIn mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension. The concept plays an important role in many parts of mathematics, including algebra and number theory — indeed in any area where fields appear prominently. Suppose that E/F is a field extension. Then E may be considered as a vector space over F (the field of scalars). The dimension of this vector space is called the degree of the field extension, and it is denoted by [E:F].
PseudogroupIn mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation of the concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example). The modern theory of pseudogroups was developed by Élie Cartan in the early 1900s.
OugandaLOuganda, en forme longue la république d'Ouganda ou la république de l'Ouganda, (en anglais : Uganda et Republic of Uganda, en swahili : Uganda et Jamhuri ya Uganda), est un pays d'Afrique de l'Est. Il est aussi considéré comme faisant partie de l'Afrique des Grands Lacs. Il est entouré par la République démocratique du Congo à l'ouest, le Kenya à l'est, le Rwanda au sud-ouest, le Soudan du Sud au nord et la Tanzanie au sud. Le Sud du pays englobe une vaste partie du lac Victoria.
Extension (semantics)In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question.
