Lectures in abstract algebra : v. 1. Basic concepts

Princeton, N. J. ; New York ; Toronto [etc] : D. Van Nostrand, , ©1951, 1962, 1962. Good. 1st ed., 6th printing ; xii, 217 pp. ; diagrams ; LCCN: 51-10909 ; OCLC: 523831; LC: QA266; Dewey: 512.89 ; ISBN: 0387901817 ; mottled worn blue cloth ; no dustjacket ; "Nathan Jacobson (October 5, 1910 — December 5, 1999) was an American mathematician. Born in Warsaw, Poland (then part of Russia) he emigrated to America with his Jewish family in 1918. Recognized as one of the leading algebraists of his generation, he was also famous for writing more than a dozen standard textbooks. He graduated from the University of Alabama in 1930 and was awarded a doctorate in mathematics from Princeton University in 1934. While working on his thesis, Non-commutative polynomials and cyclic algebras, he was advised by Joseph Wedderburn. Jacobson taught and researched at Bryn Mawr College (1935-1936), the University of Chicago (1936-1937), the University of North Carolina at Chapel Hill (1937-1943), and Johns Hopkins University (1943-1947) before joining Yale University in 1947. He remained at Yale until his retirement. ; Contents: Concepts from set theory; the system of natural numbers -- Semi-groups and groups -- Rings, integral domains and fields -- Extensions of rings and fields (polynomial rings, symmetric polynomials, rings of functions, etc) -- Elementary factorization theory (Gaussian semi-groups, principle ideal domains, Euclidean domains, etc) -- Groups with operators (Schreier's theorem, chain conditions, projections, Kull-Schmidt theorem, etc) -- Modules and ideals (Generators, unitary modules, Hilbert basis theorem, Noetherian rings, integral dependence, integers of quadratic fields, etc) -- Lattices (modular lattices, independence, Boolean algebras, etc) ; G