LEADER 04082nam 22007332 450 001 9910784305103321 005 20151005020621.0 010 $a1-107-16158-4 010 $a1-280-54067-2 010 $a9786610540679 010 $a0-511-21550-9 010 $a0-511-21729-3 010 $a0-511-21192-9 010 $a0-511-31588-0 010 $a0-511-84169-8 010 $a0-511-21369-7 035 $a(CKB)1000000000353001 035 $a(EBL)266627 035 $a(OCoLC)171139168 035 $a(SSID)ssj0000182779 035 $a(PQKBManifestationID)11156117 035 $a(PQKBTitleCode)TC0000182779 035 $a(PQKBWorkID)10172847 035 $a(PQKB)11086572 035 $a(UkCbUP)CR9780511841699 035 $a(Au-PeEL)EBL266627 035 $a(CaPaEBR)ebr10131606 035 $a(CaONFJC)MIL54067 035 $a(OCoLC)144618414 035 $a(MiAaPQ)EBC266627 035 $a(PPN)261325590 035 $a(EXLCZ)991000000000353001 100 $a20101021d2004|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn introduction to noncommutative noetherian rings /$fK.R. Goodearl, R.B. Warfield, Jr$b[electronic resource] 205 $aSecond edition. 210 1$aCambridge :$cCambridge University Press,$d2004. 215 $a1 online resource (xxiv, 344 pages) $cdigital, PDF file(s) 225 1 $aLondon Mathematical Society student texts ;$v61 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-54537-4 311 $a0-521-83687-5 320 $aIncludes bibliographical references (p. [328]-337) and index. 327 $aCover; Series-title; Title; Copyright; Contents; Introduction to the Second Edition; Introduction to the First Edition; Prologue; 1. A Few Noetherian Rings; 2. Skew Polynomial Rings; 3. Prime Ideals; 4. Semisimple Modules, Artinian Modules, and Torsionfree Modules; 5. Injective Hulls; 6. Semisimple Rings of Fractions; 7. Modules over Semiprime Goldie Rings; 8. Bimodules and A.liated Prime Ideals; 9. Fully Bounded Rings; 10. Rings and Modules of Fractions; 11. Artinian Quotient Rings; 12. Links Between Prime Ideals; 13. The Artin-Rees Property; 14. Rings Satisfying the Second Layer Condition 327 $a15. Krull Dimension16. Numbers of Generators of Modules; 17. Transcendental Division Algebras; Appendix. Some Test Problems for Noetherian Rings; Bibliography; Index 330 $aThis 2004 introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. Material includes the basic types of quantum groups, which then serve as test cases for the theory developed. 410 0$aLondon Mathematical Society student texts ;$v61. 606 $aNoetherian rings 606 $aNoncommutative rings 615 0$aNoetherian rings. 615 0$aNoncommutative rings. 676 $a512/.4 700 $aGoodearl$b K. R.$057894 702 $aWarfield$b Robert B.$f1940- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910784305103321 996 $aIntroduction to noncommutative noetherian rings$9921290 997 $aUNINA