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Serge Lang (French:; May 19, 1927 – September 12, 2005) was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra .
In abstract algebra, a multiplicatively closed set (or multiplicative set) is a subset S of a ring R such that the following two conditions hold: [1] [2], for all ,.; In other words, S is closed under taking finite products, including the empty product 1. [3]
However, Serge Lang conjectured an improvement of Roth's result; in particular he conjectured that q 2+ε in the denominator of the right-hand side could be reduced to () +. Roth's work effectively ended the work started by Liouville, and his theorem allowed mathematicians to prove the transcendence of many more numbers, such as the ...
The condition was first introduced and studied by Lang. [10] If a field is C i then so is a finite extension. [11] [12] The C 0 fields are precisely the algebraically closed fields. [13] [14] Lang and Nagata proved that if a field is C k, then any extension of transcendence degree n is C k+n.
An associative algebra A over a ring R is a graded algebra if it is graded as a ring. ... Lang, Serge (2002), Algebra, ... vol. 211 (Revised third ed.),
Chapter III.7, p.153 of Lang, Serge (1993), Algebra (Third ed.), Reading, Mass.: Addison-Wesley, ISBN 978-0-201-55540-0, Zbl 0848.13001 This linear algebra -related article is a stub . You can help Wikipedia by expanding it .
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Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with variable numbers of pages).
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