LEADER 03207nam 22005895 450 001 9910821727603321 005 20240516013509.0 010 $a1-4757-6898-2 024 7 $a10.1007/978-1-4757-6898-5 035 $a(CKB)2660000000024770 035 $a(SSID)ssj0000963215 035 $a(PQKBManifestationID)11525809 035 $a(PQKBTitleCode)TC0000963215 035 $a(PQKBWorkID)10976242 035 $a(PQKB)11352118 035 $a(DE-He213)978-1-4757-6898-5 035 $a(MiAaPQ)EBC3085353 035 $a(PPN)238081893 035 $a(EXLCZ)992660000000024770 100 $a20130427d1990 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aUndergraduate Algebra /$fby Serge Lang 205 $a2nd ed. 1990. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1990. 215 $a1 online resource (XI, 371 p.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aIncludes index. 311 $a0-387-97279-X 311 $a1-4757-6900-8 327 $aI The Integers -- II Groups -- III Rings -- IV Polynomials -- V Vector Spaces and Modules -- VI Some Linear Groups -- VII Field Theory -- VIII Finite Fields -- IX The Real and Complex Numbers -- X Sets -- §1. The Natural Numbers -- §2. The Integers -- §3. Infinite Sets. 330 $aThis book, together with Linear Algebra, constitutes a curriculum for an algebra program addressed to undergraduates. The separation of the linear algebra from the other basic algebraic structures fits all existing tendencies affecting undergraduate teaching, and I agree with these tendencies. I have made the present book self contained logically, but it is probably better if students take the linear algebra course before being introduced to the more abstract notions of groups, rings, and fields, and the systematic development of their basic abstract properties. There is of course a little overlap with the book Lin­ ear Algebra, since I wanted to make the present book self contained. I define vector spaces, matrices, and linear maps and prove their basic properties. The present book could be used for a one-term course, or a year's course, possibly combining it with Linear Algebra. I think it is important to do the field theory and the Galois theory, more important, say, than to do much more group theory than we have done here. There is a chapter on finite fields, which exhibit both features from general field theory, and special features due to characteristic p. Such fields have become important in coding theory. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aAlgebra 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 615 0$aAlgebra. 615 14$aAlgebra. 676 $a512 676 $a512 686 $a13-01$2msc 686 $a15-01$2msc 700 $aLang$b Serge$4aut$4http://id.loc.gov/vocabulary/relators/aut$01160 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910821727603321 996 $aUndergraduate algebra$983051 997 $aUNINA