04202nam 2200601 a 450 991077907440332120230802004610.0981-4365-14-9(CKB)2550000000087525(EBL)846136(SSID)ssj0000646028(PQKBManifestationID)11940162(PQKBTitleCode)TC0000646028(PQKBWorkID)10685612(PQKB)11361851(MiAaPQ)EBC846136(WSP)00008223(Au-PeEL)EBL846136(CaPaEBR)ebr10529368(CaONFJC)MIL498433(OCoLC)877768097(EXLCZ)99255000000008752520120209d2012 uy 0engur|n|---|||||txtccrGröbner bases in ring theory[electronic resource] /Huishi LiSingapore World Scientificc20121 online resource (295 p.)Description based upon print version of record.981-4365-13-0 Includes bibliographical references (p. 271-280) and index.Preface; 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-Bases3.5 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-Property5.6 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 Bases8.1 Lifting (Finite) Grobner Bases from On(λji)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; IndexThis monograph strives to introduce a solid foundation on the usage of Gröbner 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 Gröbner 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 Gröbner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finitenesGröbner basesRings (Algebra)Gröbner bases.Rings (Algebra)512.4SK 230rvkLi Huishi56176MiAaPQMiAaPQMiAaPQBOOK9910779074403321Gröbner bases in ring theory3811830UNINA