LEADER 04208nam 2200601 a 450 001 9910457538003321 005 20200520144314.0 010 $a981-4365-14-9 035 $a(CKB)2550000000087525 035 $a(EBL)846136 035 $a(SSID)ssj0000646028 035 $a(PQKBManifestationID)11940162 035 $a(PQKBTitleCode)TC0000646028 035 $a(PQKBWorkID)10685612 035 $a(PQKB)11361851 035 $a(MiAaPQ)EBC846136 035 $a(WSP)00008223 035 $a(Au-PeEL)EBL846136 035 $a(CaPaEBR)ebr10529368 035 $a(CaONFJC)MIL498433 035 $a(OCoLC)877768097 035 $a(EXLCZ)992550000000087525 100 $a20120209d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGro?bner bases in ring theory$b[electronic resource] /$fHuishi Li 210 $aSingapore $cWorld Scientific$dc2012 215 $a1 online resource (295 p.) 300 $aDescription based upon print version of record. 311 $a981-4365-13-0 320 $aIncludes bibliographical references (p. 271-280) and index. 327 $aPreface; Contents; 0. Introduction; 1. Preliminaries; 1.1 Presenting Algebras by Relations; 1.2 S-Graded Algebras and Modules; 1.3 -Filtered Algebras and Modules; 2. The -Leading Homogeneous Algebra A LH; 2.1 Recognizing A via G (A): Part 1; 2.2 Recognizing A via G (A): Part 2; 2.3 The -Graded Isomorphism A LH G (A); 2.4 Recognizing A via A LH; 3. Grobner Bases: Conception and Construction; 3.1 Monomial Ordering and Admissible System; 3.2 Division Algorithm and Grobner Basis; 3.3 Grobner Bases and Normal Elements; 3.4 Grobner Bases w.r.t. Skew Multiplicative K-Bases 327 $a3.5 Grobner Bases in KhX1, . . . ,Xni and KQ3.6 (De)homogenized Grobner Bases; 3.7 dh-Closed Homogeneous Grobner Bases; 4. Grobner Basis Theory Meets PBW Theory; 4.1 -Standard Basis and -PBW Isomorphism; 4.2 Realizing - PBW Isomorphism by Grobner Basis; 4.3 Classical PBW K-Bases vs Grobner Bases; 4.4 Solvable Polynomial Algebras Revisited; 5. Using AB LH in Terms of Grobner Bases; 5.1 The Working Strategy; 5.2 Ufnarovski Graph; 5.3 Determination of Gelfand-Kirillov Dimension; 5.4 Recognizing Noetherianity; 5.5 Recognizing (Semi-)Primeness and PI-Property 327 $a5.6 Anick's Resolution over Monomial Algebras5.7 Recognizing Finiteness of Global Dimension; 5.8 Determination of Hilbert Series; 6. Recognizing (Non-)Homogeneous p-Koszulity via ABLH; 6.1 (Non-)Homogeneous p-Koszul Algebras; 6.2 Anick's Resolution and Homogeneous p-Koszulity; 6.3 Working in Terms of Grobner Bases; 7. A Study of Rees Algebra by Grobner Bases; 7.1 Defining A by G*; 7.2 Defining A by G; 7.3 Recognizing Structural Properties of A via G; 7.4 An Application to Regular Central Extensions; 7.5 Algebras Defined by dh-Closed Homogeneous Grobner Bases; 8. Looking for More Grobner Bases 327 $a8.1 Lifting (Finite) Grobner Bases from On(?ji)8.2 Lifting (Finite) Grobner Bases from a Class of Algebras; 8.3 New Examples of Grobner Basis Theory; 8.4 Skew 2-Nomial Algebras; 8.5 Almost Skew 2-Nomial Algebras; Bibliography; Index 330 $aThis monograph strives to introduce a solid foundation on the usage of Gro?bner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Gro?bner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Gro?bner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finitenes 606 $aGro?bner bases 606 $aRings (Algebra) 608 $aElectronic books. 615 0$aGro?bner bases. 615 0$aRings (Algebra) 676 $a512.4 700 $aLi$b Huishi$056176 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910457538003321 996 $aGro?bner bases in ring theory$92447618 997 $aUNINA