Titlebook: Lectures in Abstract Algebra I; Basic Concepts Nathan Jacobson Textbook 1951 Nathan Jacobson 1951 Galois theory.Permutation.algebra.automor

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Lattices,subgroups, ideals) of these systems rather than with the elements themselves. This is particularly true of the Jordan-Hölder-Schreier theory. Here the arguments concern the system of .-subgroups and the compositions in this system of intersection and group generated. Similarly, parts of the theory o

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Elementary Factorization Theory,= .. Since the factorization theory that we shall consider is a purely multiplicative theory that concerns the semi-group of non-zero elements of a commutative integral domain, we shall find it clearer to begin our discussion with the factorization theory of semi-groups.

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Textbook 1951tures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale "University. The general plan of the work IS as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the

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Rings, Integral Domains and Fields, isomorphism, homomorphism and anti-isomorphism. Also we introduce some important special instances of rings such as matrix rings and quaternions. Finally we prove the analogue for rings of Cayley’s theorem on groups.

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Extensions of Rings and Fields,pter. Among others we define also rings of polynomials, field extensions and rings of functions. We derive some of the properties of these extensions and, in particular, we determine the algebraic structure of any field.

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Lattices, the foundations of geometry and to other fields have been discovered. It should be noted also that prior to Dedekind’s work a special class of lattices, Boolean algebras, had been introduced by Boole.

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Textbook 1951g of many. The second and third volumes of this work will be more special­ ized in nature and will attempt to give comprehensive accounts of the topics which they treat. Volume II will bear the title Linear Algebra and will deal with the theorv of vectQ!_JlP. -a. ces. . . . . Volume III, The Theory