Rings and Things and a Fine Array of Twentieth Century Associative AlgebraAmerican Mathematical Soc., 2004 - 475 páginas This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. Included in the book are certain categorical properties from theorems of Frobenius and Stickelberger on the primary decomposition of finite Abelian formulations of the latter by Krull, Goldman, and others; Maschke's theorem on the representation theory of finite groups over a field; and the fundamental theorems of Wedderburn on the structure of finite dimensional algebras Goldie, and others. A special feature of the book is the in-depth study of rings with chain condition on annihilator ideals pioneered by Noether, Artin, and Jacobson and refined and extended by many later mathematicians. Two of the author's prior works, Algebra: Rings, Modules and Categories, I and II (Springer-Verlag, 1973), are devoted to the development of modern associative algebra and ring and module theory. Those bibliography of over 1,600 references and is exhaustively indexed. In addition to the mathematical survey, the author gives candid and descriptive impressions of the last half of the twentieth century in ''Part II: Snapshots of fellow graduate students at the University of Kentucky and at Purdue, Faith discusses his Fulbright-Nato Postdoctoral at Heidelberg and at the Institute for Advanced Study (IAS) at Princeton, his year as a visiting scholar at Berkeley, and the many acquaintances he met there and in subsequent travels in India, Europe, and most recently, Barcelona. Comments on the first edition: ''Researchers in algebra should find it both full references as to the origin and development of the theorem ... I know of no other work in print which does this as thoroughly and as broadly.'' --John O'Neill, University of Detroit at Mercy '' 'Part II: Snapshots of Mathematicians of my age and younger will relish reading 'Snapshots'.'' --James A. Huckaba, University of Missouri-Columbia |
Índice
Part I An Array of Twentieth Century Associative Algebra | 1 |
Part II Snapshots of Some Mathematical Friends and Places | 285 |
| 365 | |
Bibliography | 371 |
Otras ediciones - Ver todo
Rings and Things and a Fine Array of Twentieth Century Associative Algebra Carl Faith Vista de fragmentos - 1999 |
Rings and Things and a Fine Array of Twentieth Century Associative Algebra Carl Clifton Faith No hay ninguna vista previa disponible |
Términos y frases comunes
Abelian group algebraically closed Amer Amitsur Artinian ring associated prime automorphisms cogenerator Cohn commutative ring contains COROLLARY countable cyclic Dedekind denote direct sum direct summand eatension endomorphism ring equivalent field finite dimensional finite product FP-injective FPF rings Galois global dimension Goldie dimension Goodearl group G group ring hence ibid idempotent indecomposable injective hull injective module injective right isomorphic Jacobson radical Kaplansky Kasch Krull dimension Lemma linearly compact loc.cit marimal maſcimal Math mathematics matrix ring maximal ideal Menal mod-R Morita n x n nilpotent Noetherian ring nonzero op.cit polynomial ring prime ideal Princeton Proc projective PROOF Prüfer pure-injective quasi-injective quotient ring REMARK resp right and left right Artinian right Goldie right ideal right Noetherian right R-module right self-injective Rutgers satisfies self-injective ring semilocal semiperfect semiprime semisimple simple ring submodule subring THEOREM FAITH valuation ring Vámos VNR ring zero divisors