Abelian Groups (International Series in Pure and Applied by L. Fuchs,J. P. Kahane,A. P. Robertson,S. Ulam

By L. Fuchs,J. P. Kahane,A. P. Robertson,S. Ulam

Abelian teams bargains with the speculation of abelian or commutative teams, with particular emphasis on effects relating constitution difficulties. greater than 500 workouts of various levels of hassle, with and with no tricks, are integrated. a few of the routines light up the theorems mentioned within the textual content by way of offering substitute advancements, proofs or counterexamples of generalizations.

Comprised of sixteen chapters, this quantity starts with an summary of the elemental evidence on staff conception reminiscent of issue workforce or homomorphism. The dialogue then turns to direct sums of cyclic teams, divisible teams, and direct summands and natural subgroups, in addition to Kulikov's easy subgroups. next chapters specialize in the constitution concept of the 3 major periods of abelian teams: the first teams, the torsion-free teams, and the combined teams. functions of the idea also are thought of, besides different themes comparable to homomorphism teams and endomorphism earrings; the Schreier extension idea with a dialogue of the crowd of extensions and the constitution of the tensor product. additionally, the ebook examines the idea of the additive staff of jewelry and the multiplicative team of fields, besides Baer's idea of the lattice of subgroups.

This ebook is meant for younger study staff and scholars who intend to familiarize themselves with abelian groups.

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