03494nam 22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202082001200225100002400237245007500261264004600336300003600382336002600418337002600444338003600470347002400506490004500530505026700575520174900842650001702591650001302608650002302621650002102644650001702665650001302682650003602695710003402731773002002765776003602785830004502821856004802866912001402914999001902928952007702947978-0-387-48899-8DE-He21320180115171408.0cr nn 008mamaa100301s2007 xxu| s |||| 0|eng d a97803874889989978-0-387-48899-87 a10.1007/978-0-387-48899-82doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh04a5122231 aLam, T. Y.eauthor.10aExercises in Modules and Ringsh[electronic resource] /cby T. Y. Lam. 1aNew York, NY :bSpringer New York,c2007. aXVIII, 414 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aProblem Books in Mathematics,x0941-35020 aFree Modules, Projective, and Injective Modules -- Flat Modules and Homological Dimensions -- More Theory of Modules -- Rings of Quotients -- More Rings of Quotients -- Frobenius and Quasi-Frobenius Rings -- Matrix Rings, Categories of Modules and Morita Theory. aFor the Backcover This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flat modules, homological and uniform dimensions, noncommutative localizations and Goldie$1 (Bs theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Morita$1 (Bs classical theory of category dualities and equivalences. Each of the nineteen sections begins with an introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail; many are accompanied by pertinent historical and bibliographical information, or a commentary on possible improvements, generalizations, and latent connections to other problems. This volume is designed as a problem book for the author$1 (Bs Lectures on Modules and Rings (Springer GTM, Vol. 189), from which the majority of the exercises were taken. Some forty new exercises have been added to further broaden the coverage. As a result, this book is ideal both as a companion volume to Lectures, and as a source for independent study. For students and researchers alike, this book will also serve as a handy reference for a copious amount of information in algebra and ring theory otherwise unavailable from textbooks. An outgrowth of the author$1 (Bs lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classical Ring Theory (Springer, 2003) offer to the mathematics community the fullest and most comprehensive reference to date for problem solving in the theory of modules and rings.s 0aMathematics. 0aAlgebra. 0aAssociative rings. 0aRings (Algebra).14aMathematics.24aAlgebra.24aAssociative Rings and Algebras.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387988504 0aProblem Books in Mathematics,x0941-350240uhttp://dx.doi.org/10.1007/978-0-387-48899-8 aZDB-2-SMA c369519d369519 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK