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Discriminants in Algebra and Arithmetic - Ghorpade (2000) (Correct)
....familiarity with the concepts such as rings, elds, vector spaces, and basic facts concerning them. We begin with a brief discussion of the notion of trace, and some of its properties, which are needed later. For proofs of these auxiliary results, one may refer to [6] or standard texts such as [10]. Let K be a eld and L be a ring containing K as a subring. Then L is a vector space over K. We will assume that the vector space dimension of L over K is nite and denote it by n. A nice passage from L to K is provided by the trace map Tr L=K : L K which is de ned as follows. Given any 2 ....
S. Lang, Algebra, 2nd ed., Addison-Wesley, 1984.
Normal Bases over Finite Fields - Gao (1993) (2 citations) (Correct)
....by Hensel [61] in 1888. The normal basis theorem for Galois extension of arbitrary fields was proved by Noether [104] in 1932 and Deuring [40] in 1933. This theorem is included in most algebra textbooks, see for example, Albert [7] Bourbaki [27] Cohn [36] Hungerford [64] Jacobson [69] Lang [78], Redei [112] and van der Waerden [141] For di#erent proofs of the normal basis theorem, see Artin [8] Berger and Reiner [15] Krasner [76] Waterhouse [149] and Childs and Orzech [33] Lenstra [86] generalizes the normal basis theorem to infinite Galois extensions. Bshouty and Seroussi [29] and ....
S. Lang, Algebra, 2nd ed., Addison-Wesley, Menlo Park, California, 1984.
Anisotropic Branching Random Walks On Homogeneous Trees - Hueter, Lalley (1999) (2 citations) (Correct)
.... F x (z) and G(z) is an algebraic function, i.e. that it satisfies a polynomial equation with coefficients in the ring C [z] This polynomial may be obtained by a straightforward elimination algorithm: to obtain F i , eliminate the other variables F j one at a time by taking resultants (see, e.g. [12]) For example, when d = 2 (in which case there are two distinct generating functions, F a (z) and F b (z) the polynomial equation satisfied by w = F i , i = a; b, is w 4 z 3 ( Gamma6p 3 i 3p 2 i ) w 3 z 2 (8p 2 i Gamma 4p i ) w 2 z 3 (4p 3 i Gamma 10p 2 i 6p i ....
Lang, S. (1984) Algebra, 2nd ed. Addison-Wesley, Reading MA.
Tameness in Expansions of the Real Field - Miller (2002) (Correct)
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S. Lang, Algebra, 2nd ed., Addison-Wesley, 1984.
Tameness in Expansions of the Real Field - Miller (2001) (Correct)
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S. Lang, Algebra, 2nd ed., Addison-Wesley, 1984.
Expansive Subdynamics for Algebraic ...-Actions - Einsiedler, Lind, Miles, Ward (Correct)
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Serge Lang, Algebra, 2nd Ed., Addison-Wesley, Menlo Park, 1984.
The Space Of Rational Maps On ... - Silverman (1996) (Correct)
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S. Lang, Algebra, 2nd ed., Addison-Wesley, Menlo Park, 1984.
K-Loops from Matrix Groups over Ordered Fields I - Kiechle (1995) (Correct)
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S. Lang, Algebra, 2 nd ed. Addison-Wesley, Reading, Massachusetts 1984.
Expansive Subdynamics for Algebraic ...-Actions - Einsiedler, Lind, Miles, Ward (2000) (Correct)
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Serge Lang, Algebra, 2nd Ed., Addison-Wesley, Menlo Park, 1984.
Low Complexity Multiplication in Rings - Silverman (Correct)
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S. Lang, Algebra, 2nd ed., Addison-Wesley (1984).
What is a Closed-Form Number? - Chow (Correct)
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S. Lang, Algebra, 2nd ed., Addison-Wesley, 1984.
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