Fundamental exponents in the theory of algebraic numbers
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Fundamental exponents in the theory of algebraic numbers

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Published by [s.n.] in Toronto .
Written in English


Book details:

Edition Notes

Thesis (Ph.D.)--University of Toronto, 1937.

StatementDavid Carruthers Murdoch.
ID Numbers
Open LibraryOL15051708M

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Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their -theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function properties, such as whether a ring admits. Honors Abstract Algebra. This note describes the following topics: Peanos axioms, Rational numbers, Non-rigorous proof of the fundamental theorem of algebra, polynomial equations, matrix theory, Groups, rings, and fields, Vector spaces, Linear maps and the dual space, Wedge products and some differential geometry, Polarization of a polynomial, Philosophy of the Lefschetz theorem, Hodge star. The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero.. Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed. In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.