abstract algebra oor Sjinees
abstract algebra
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(mathematics) The branch of mathematics concerned with algebraic structures, such as groups, rings, and fields.
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math
抽象代數
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抽象代数学
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抽象代數學
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Dickson had a major impact on American mathematics, especially abstract algebra.
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Both rules are wholly familiar from school mathematics and from abstract algebra generally.
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Abstract algebraic logic has become a well established subfield of algebraic logic, with many deep and interesting results.
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Finally, prime ideal theorems do also exist for other (not order-theoretical) abstract algebras.
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The two main motivations for the development of abstract algebraic logic are closely connected to (1) and (3) above.
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Ideals were introduced first by Marshall H. Stone, who derived their name from the ring ideals of abstract algebra.
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Abstract algebra was developed in the 19th century, deriving from the interest in solving equations, initially focusing on what is now called Galois theory, and on constructibility issues.
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(One should keep in mind that in Grassmann's day, the only axiomatic theory was Euclidean geometry, and the general notion of an abstract algebra had yet to be defined.)
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Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory, computational complexity, statistics, combinatorics, abstract algebra, number theory, and finite mathematics generally.
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This GCD definition led to the modern abstract algebraic concepts of a principal ideal (an ideal generated by a single element) and a principal ideal domain (a domain in which every ideal is a principal ideal).
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Abstract algebraic logic is a modern subarea of algebraic logic that emerged in Poland during the 1950s and 60s with the work of Helena Rasiowa, Roman Sikorski, Jerzy Łoś, and Roman Suszko (to name but a few).
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Perhaps the most important achievement of abstract algebraic logic has been the classification of propositional logics in a hierarchy, called the abstract algebraic hierarchy or Leibniz hierarchy, whose different levels roughly reflect the strength of the ties between a logic at a particular level and its associated class of algebras.
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In more abstract language, the spectral theorem is a statement about commutative C*-algebras.
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Despite his age he became a student and his first interest was in abstract algebra.
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The Galois Theory and Group Theory that he studied had become important branches of Abstract Algebra.
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The extension of an object in abstract algebra , such as a group , is the underlying set of the object.
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For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations.
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Mac Lane had been at Harvard during 1934-36 and in 1937 Birkhoff taught his first undergraduate course on abstract algebra.
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At that time Emmy Noether was in Moscow and gave a course at Moscow State University on abstract algebra, which Aleksandrov attended.
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Abstract algebra, an advanced-level textbook of modern algebra, was first published in 1932 and it proved a very significant work for Japanese mathematics.
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... is a continuation of a long series of articles by [Foster ] and his students which investigates unique factorization in certain classes of abstract algebras.
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What we recognise in undergraduate courses in algebra today took much of its start with the abstract algebra which they made both accessible and attractive.
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At first he was supervised on mathematical physics at Cambridge but, with a growing interest in abstract algebra, he changed supervisors to work with Philip Hall .
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Abel and Galois's investigations into the solutions of various polynomial equations laid the groundwork for further developments of group theory , and the associated fields of abstract algebra .
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Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra .
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