principal ideal domain
주 아이디얼 정역
principal ideal oor Koreaans
principal ideal
en
(algebra) An ideal which is generated by a single element of the ring.
Vertalings in die woordeboek Engels - Koreaans
주 아이디얼
en
ideal generated by one element
Geskatte vertalings
Vertoon algoritmies gegenereerde vertalings
Soortgelyke frases
voorbeelde
Advanced filtering
Voorbeelde moet herlaai word.
He studied local rings and semilocal rings and proved certain results on principal ideal domains.
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Iyanaga managed to solve a question of Artin on generalising the principal ideal theorem and this was published in 1939. He wrote :
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One of the first papers which he published after arriving in the United States was on the Euclidean algorithm in principal ideal domains.
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... covers the basic facts of algebraic number theory starting with the divisibility theory in principal ideal domains and ending with the unit theorem, finiteness of the class number and the more elementary theorems of the Hilbert ramification theory.
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Similarly, Artin's Reciprocity Law opens the way to new applications and progress.The most striking application was given by Furtwängler's proof of the principal ideal theorem of class field theory, given one year after the publication of Artin's Reciprocity Law.
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In passing from the finite to the infinite case Krull introduced topological ideas. In 1928 he defined the Krull dimension of a commutative Noetherian ring and brought ring theory into in new setting in which he was able to show that the principal ideal theorem held.
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This involves studying the ring of integer quaternions in which there are 24 units. He shows that one-sided ideals are principal and introduces prime and primary quaternions.
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7 sinne gevind in 8 ms. Hulle kom uit baie bronne en word nie nagegaan nie.