prime extension
31India — /in dee euh/, n. 1. Hindi, Bharat. a republic in S Asia: a union comprising 25 states and 7 union territories; formerly a British colony; gained independence Aug. 15, 1947; became a republic within the Commonwealth of Nations Jan. 26, 1950.… …
32Algebraic 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… …
33Going up and going down — In commutative algebra, a branch of mathematics, going up and going down are terms which refer to certain properties of chains of prime ideals in integral extensions. The phrase going up refers to the case when a chain can be extended by upward… …
34United Kingdom — a kingdom in NW Europe, consisting of Great Britain and Northern Ireland: formerly comprising Great Britain and Ireland 1801 1922. 58,610,182; 94,242 sq. mi. (244,100 sq. km). Cap.: London. Abbr.: U.K. Official name, United Kingdom of Great… …
35education — /ej oo kay sheuhn/, n. 1. the act or process of imparting or acquiring general knowledge, developing the powers of reasoning and judgment, and generally of preparing oneself or others intellectually for mature life. 2. the act or process of… …
36Chebotarev's density theorem — in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field Q of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic… …
37china — /chuy neuh/, n. 1. a translucent ceramic material, biscuit fired at a high temperature, its glaze fired at a low temperature. 2. any porcelain ware. 3. plates, cups, saucers, etc., collectively. 4. figurines made of porcelain or ceramic material …
38China — /chuy neuh/, n. 1. People s Republic of, a country in E Asia. 1,221,591,778; 3,691,502 sq. mi. (9,560,990 sq. km). Cap.: Beijing. 2. Republic of. Also called Nationalist China. a republic consisting mainly of the island of Taiwan off the SE coast …
39Russia — /rush euh/, n. 1. Also called Russian Empire. Russian, Rossiya. a former empire in E Europe and N and W Asia: overthrown by the Russian Revolution 1917. Cap.: St. Petersburg (1703 1917). 2. See Union of Soviet Socialist Republics. 3. See Russian… …
40United States — a republic in the N Western Hemisphere comprising 48 conterminous states, the District of Columbia, and Alaska in North America, and Hawaii in the N Pacific. 267,954,767; conterminous United States, 3,022,387 sq. mi. (7,827,982 sq. km); with… …
