Collected Mathematical Papers: Vol. 1: 1934-1946

ISBN-13: 9781461282143 / Angielski / Miękka / 2012 / 454 str.

N. Jacobson

Opis

This collection contains all my published papers, both research and expository, that were published from 1934 to 1988. The research papers arranged in chronological order appear in Volume I and II and in the first part of Volume III. The expository papers, which are mainly reports presented at conferences, appear in chronological order in the last part of Volume III. Volume I covers the period 1910 to 1947, the year I moved to Yale, Volume II covers the period 1947 to 1965 when I became Chairman of the Department at Yale and Volume III covers the period from 1965 to 1989, which goes beyond my assumption of an emeritus status in 1981. I have divided the time interval covered in each volume into subintervals preceded by an account of my personal history during this period, and a commentary on the research papers published in the period. I have omitted commentaries on the expository papers and have sorted out the commentaries on the research papers according to the principal fields of my research. my recollections, checked against written The personal history has been based on documentation in my file of letters as well as diaries. One of these was a diary I kept of my trip to the USSR in 1961; the others were diaries Florie (Florence) kept during other major visits abroad. I have also consulted Professor A. W. Tucker on historical details on Princeton during the 1930's.

Spis treści

Personal History and Commentary (1910–1943).- Research Papers, 1934–1943.- [1] Non-commutative polynomials and cyclic algebras.- [2] A note on non-commutative polynomials.- [3] Locally compact rings (with O. Taussky).- [4] Rational methods in the theory of Lie algebras.- [5] On pseudo-linear transformations.- [6] Totally disconnected locally compact rings.- [7] Simple Lie algebras of type A.- [8] Pseudo-linear transformations.- [9] A class of normal simple Lie algebras of characteristic zero.- [10] A note on non-associative algebras.- [11] Abstract derivation and Lie algebras.- [12] p-Algebras of exponent p.- [13] A note on topological fields.- [14] Simple Lie algebras of type A.- [15] Simple Lie algebras over a field of characteristic zero.- [16] Normal semi-linear transformations.- [17] An application of E. H. Moore’s determinant of a Hermitian matrix.- [18] Structure and automorphisms of semi-simple Lie groups in the large.- [19] Cayley numbers and normal simple Lie algebras of type G.- [20] The fundamental theorem of the Galois theory for quasi-fields.- [21] A note on hermitian forms.- [22] Restricted Lie algebras of characteristic p.- [23] Classes of restricted Lie algebras of characteristic p I.- [24] Classes of restricted Lie algebras of characteristic p II.- Personal History and Commentary (1943–1946).- Research Papers, 1943–1946.- [25] An extension of Galois theory to non-normal and non-separable fields.- [26] Schur’s theorems on commutative matrices.- [27] Relations between the composites of a field and those of a subfield.- [28] Galois theory of purely inseparable fields of exponent one.- [29] Construction of central simple associative algebras.- [30] The equation x ’ ? xd-dx = b.- [31] Structure theory of simple rings without finiteness assumptions.- [32] The radical and semi-simplicity for arbitrary rings.- [33] Structure theory for algebraic algebras of bounded degree.- [34] A topology for the set of primitive ideals in an arbitrary ring.- [35] On the theory of primitive rings.- [36] A note on division rings.- [37] Isomorphisms of Jordan rings.- [38] The center of a Jordan ring.- Permissions.