ramified ideal
1Different ideal — In algebraic number theory, the different ideal (sometimes simply the different) is defined to account for the (possible) lack of duality in the ring of integers of an algebraic number field K, with respect to the field trace. It was introduced… …
2Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …
3Splitting of prime ideals in Galois extensions — In mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of prime ideals of OL, provides one of the richest parts of… …
4Discriminant of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… …
5Eisenstein's criterion — In mathematics, Eisenstein s criterion gives sufficient conditions for a polynomial to be irreducible over the rational numbers (or equivalently, over the integers; see Gauss s lemma). Suppose we have the following polynomial with integer… …
6Europe, history of — Introduction history of European peoples and cultures from prehistoric times to the present. Europe is a more ambiguous term than most geographic expressions. Its etymology is doubtful, as is the physical extent of the area it designates.… …
7YIDDISH LITERATURE — This articles is arranged according to the following outline: introduction UNTIL THE END OF THE 18TH CENTURY the bible in yiddish literature epic homiletic prose drama liturgy ethical literature Historical Songs and Writings transcriptions of… …
8logic, history of — Introduction the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic There was a medieval tradition according to which the Greek philosopher …
9Islāmic world — Introduction prehistory and history of the Islamic community. Adherence to Islām is a global phenomenon: Muslims predominate in some 30 to 40 countries, from the Atlantic to the Pacific and along a belt that stretches across northern… …
10Western architecture — Introduction history of Western architecture from prehistoric Mediterranean cultures to the present. The history of Western architecture is marked by a series of new solutions to structural problems. During the period from the… …
