Эрнст Куммер тщетно пытался доказать Великую теорему Ферма, и его метод (аналогичный собственному Ферма) не удался, потому что не все кольца обладают «красивым» свойством уникальной факторизации. Изучение этих уникальных областей факторизации не привело к доказательству Великой теоремы Ферма, но привело к их изучению:
1. Алгебраические числа
2. идеалы
3. простые числа
4. кольцевые генераторы
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Ernst Kummer tried in vain to prove Fermat's Last Theorem, and his method (similar to Fermat's own) broke down because not all rings have the "nice" property of unique factorization. Studying these unique factorization domains did not lead to a proof of Fermat's Last Theorem, but it did lead to the study of these:
1. Algebraic numbers
2. ideals
3. prime numbers
4.ring generators
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Ernst Eduard Kummer, (born January 29, 1810, Sorau, Brandenburg, Prussia [Germany]—died May 14, 1893, Berlin), German mathematician whose introduction of ideal numbers, which are defined as a special subgroup of a ring, extended the fundamental theorem of arithmetic (unique factorization of every integer into a product of primes) to complex number fields.
Germany encompasses a wide variety of landscapes: the tall, sheer mountains of the south; the sandy, rolling plains of the north; the forested hills of the urbanized west; and the plains of the agricultural east. At the spiritual heart of the country is the magnificent east-central city of Berlin, which rose phoenixlike from the ashes of World War II and now, after decades of partition, is the capital of a reunified Germany, and the Rhine River, which flows northward from Switzerland and is celebrated in visual art, literature, folklore, and song. Along its banks and those of its principal tributaries—among them the Neckar, Main, Moselle, and Ruhr—stand hundreds of medieval castles, churches, picturesque villages, market towns, and centres of learning and culture, including Heidelberg, the site of one of Europe’s oldest universities (founded in 1386), and Mainz, historically one of Europe’s most important publishing centres. All are centrepieces of Germany’s thriving tourist economy, which brings millions of visitors to the country each year, drawn by its natural beauty, history, culture, and cuisine (including its renowned wines and beersSince World War II, Germany has made great efforts to both commemorate the victims and redress the crimes of the Holocaust, providing strong material and political support for the state of Israel and actively prosecuting hate crimes and the propagation of neo-Nazi doctrine; the latter became an issue in the 1990s with the rise in Germany of anti-immigrant skinhead groups and the availability of Hitler’s Mein Kampf over the Internet. Clearly, modern Germany struggles to balance its national interests with those of an influx of political and economic refugees from far afield, especially North Africa, Turkey, and South Asia, an influx that has fueled ethnic tensions and swelled the ranks of nationalist political parties, particularly in eastern Germany, where unemployment was double that of the west. Tensions became especially acute in the second decade of the 21st century, when more than one million migrants entered Germany in the wake of the revolutions of the Arab Spring and the Syrian Civil War.
Know about the history behind the making of Berlin rather than Bonn, the capital of reunified Germany
Know about the history behind the making of Berlin rather than Bonn, the capital of reunified Germany
Overview of the decision to make Berlin—rather than Bonn—the capital of reunified Germany.
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The constitution of the republic, adopted in 1949 by West Germany, created a federal system that gives significant government powers to its constituent Länder (states). Before unification there were 11 West German Länder (including West Berlin, which had the special status of a Land without voting rights), but, with the accession of East Germany, there are now 16 Länder in the unified republic. The largest of the states is Bavaria (Bayern), the richest is Baden-Württemberg, and the most populous is North Rhine–Westphalia (Nordrhein-Westfalen).
Matters of national importance, such as defense and foreign affairs, are reserved to the federal government. At both the state and federal levels, parliamentary democracy prevails. The Federal Republic has been a member of the North Atlantic Treaty Organization (NATO) since 1955 and was a founding member of the European Economic Community (see European Union). During the four decades of partition, the Federal Republic concluded a number of agreements with the Soviet Union and East Germany, which it supported to some extent economically in return for various concessions with regard to humanitarian matters and access to Berlin. West Germany’s rapid economic recovery in the 1950s (Wirtschaftswunder, or “economic miracle”) brought it into a leading position among the world’s economic powers, a position that it has maintained.
Much of Germany’s post-World War II success has been the result of the renowned industriousness and self-sacrifice of its people, about which novelist Günter Grass, winner of the Nobel Prize for Literature in 1999, remarked, “To be a German is to make the impossible possible.” He added, more critically,
For in our country everything is geared to growth. We’re never satisfied. For us enough is never enough. We always want more. If it’s on paper, we convert it into reality. Even in our dreams we’re productive.