Pollack introduces algebraic number theory to readers who are familiar with linear algebra, commutative ring theory, Galois theory, a little abelian groups
theory, and elementary number theory up to and including the law of quadratic reciprocity.
Examples of such groups are: finite Abelian groups
(, Theorem 4.
In fact for abelian groups
(and much more general situations) we have by Schauenburg [Schau02] a Kunneth-type formula, and this decomposition does precisely explain the initially observed decomposition.
They discuss modules, including vector spaces and abelian groups
, group theory, and quasigroups.
digital representations of real numbers), and for recognizing some sets of integers or more generally of finitely generated abelian groups
Lehmer, A ternary analogue of abelian groups
, American Journal of Mathematics, 59 (1932) 329-338.
Among the topics are greatest common divisors, integer multiples and exponents, quotients of polynomial rings, divisibility and factorization in integral domains, subgroups of cyclic groups, cosets and Lagrange's theorem, the fundamental theorem of finite abelian groups
, and check digits.
1 (Fundamental theorem of finite abelian groups
) Any finite abelian group
G can be written as a direct sum of cyclic groups in the following canonical way: G = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where every [k.
A quasi-arithmetic matroid endows a matroid with a multiplicity function, whose values (in the representable case) are the cardinalities of certain finite abelian groups
, namely, the torsion parts of the quotients of an ambient lattice [Z.
Infinite Abelian Groups
Vol 1 New York: Academic Press.
We define a(n) to be the number of nonisomorphic Abelian groups
with n elements.
Their topics include financial markets, polynilpotent multipliers of finitely generated abelian groups
, the concept of subtype in Bernstein algebras, optimal processes in irreversible microeconomics, algebraic solutions for matrix games, methods of drawing special curves and surfaces, some game theory and financial contracting issues in large corporate transactions, endomorphisms and endomorphism semigroups of groups, the noiseless coding theorem, odd zeta and other special function bounds, and spectral properties of discrete Schrodinger operator with quasi-periodically recurrent potential.