NONCOMMUTATIVE GRÖBNER BASES AND FILTERED-GRADED TRANSFER
CONTENTS INTRODUCTION CHAPTER I BASIC STRUCTURAL TRICKS AND EXAMPLES 1 ALGEBRAS AND THEIR DE?NING RELATIONS 2 SKEW POLYNOMIAL RINGS 3 ZZ-?LTRATIONS AND THEIR ASSOCIATED GRADED STRUCTURES 4 HOMOGENIZATION AND DEHOMOGENIZATION OF ZZ-GRADED RINGS 5 SOME ALGEBRAS: CLASSICAL AND MODERN CHAPTER II GR¨OBNER BASES IN ASSOCIATIVE ALGEBRAS 1 (LEFT) MONOMIAL ORDERINGS AND (LEFT) ADMISSIBLE SYSTEMS 2 (LEFT) QUASI-ZERO ELEMENTS AND A (LEFT) DIVISION ALGORITHM 3 (LEFT) GR¨OBNER BASES IN A (LEFT) ADMISSIBLE SYSTEM 4 (LEFT) GR¨OBNER BASES IN VARIOUS CONTEXTS 5 (LEFT) S-ELEMENTS AND BUCHBERGER THEOREM 6 (LEFT) DICKSON SYSTEMS AND (LEFT) G-NOETHERIAN ALGEBRAS 7 SOLVABLE POLYNOMIAL ALGEBRAS 8 NO (LEFT) MONOMIAL ORDERING EXISTING ON ?(K[X1, , XN]) WITH CHARK > CHAPTER III GR¨OBNER BASES AND BASIC ALGEBRAIC-ALGORITHMIC STRUCTURES 1 PBW BASES OF FINITELY GENERATED ALGEBRAS 2 QUADRIC SOLVABLE POLYNOMIAL ALGEBRAS 3 ASSOCIATED HOMOGENEOUS DE?NING RELATIONS OF ALGEBRAS 4 A REMARK ON RECOGNIZABLE PROPERTIES OF ALGEBRAS VIA GR¨OBNER BASES CHAPTER IV FILTERED-GRADED TRANSFER OF GR¨OBNER BASES 1 FILTERED-GRADED TRANSFER OF (LEFT) ADMISSIBLE SYSTEMS 2 FILTERED-GRADED TRANSFER OF (LEFT) GR¨OBNER BASES 3 FILTERED-GRADED TRANSFER OF (LEFT) DICKSON SYSTEMS 4 FILTERED-GRADED TRANSFER APPLIED TO QUADRIC SOLVABLE POLYNOMIAL ALGEBRAS CHAPTER V GK-DIMENSION OF MODULES OVER QUADRIC SOLVABLE POLYNOMIAL ALGEBRAS AND ELIMINATION OF VARIABLES 1 GR¨OBNER BASES IN HOMOGENEOUS SOLVABLE POLYNOMIAL ALGEBRAS 2 THE HILBERT FUNCTION OF A/L 3 THE HILBERT POLYNOMIAL OF A/L 4 GK-DIMENSION COMPUTATION AND ELIMINATION OF VARIABLES (HOMOGENEOUS CASE ) 5 GK-DIMENSION COMPUTATION AND ELIMINATION OF VARIABLES (LINEAR CASE) 6 THE ?GR-?LTRATION ON A QUADRIC SOLVABLE POLYNOMIAL ALGEBRA 7 GK-DIMENSION COMPUTATION AND ELIMINATION OF VARIABLES (GENERAL QUADRIC CASE) 8 FINITE DIMENSIONAL CYCLIC MODULES CHAPTER VI MULTIPLICITY COMPUTATION OF MODULES OVER QUADRIC SOLVABLE POLYNOMIAL ALGEBRAS 1 THE MULTIPLICITY E(M) OF A MODULE M 2 COMPUTATION OF E(M) 3 COMPUTATION OF GK DIM(M ?K N) AND E(M ?K N) 4 AN APPLICATION TO AN(Q1, , QN) CHAPTER VII (?-)HOLONOMIC MODULES AND FUNCTIONS OVER QUADRIC SOLVABLE POLYNOMIAL ALGEBRAS 1 SOME OPERATOR ALGEBRAS 2 HOLONOMIC FUNCTIONS 3 AUTOMATIC PROVING OF HOLONOMIC FUNCTION IDENTITIES 4 EXTENSION/CONTRACTION OF THE ?-?NITENESS 5 THE ?-HOLONOMICITY CHAPTER VIII REGULARITY AND K0-GROUP OF QUADRIC SOLVABLE POLYNOMIAL ALGEBRAS 1 TAME CASE: A IS AUSLANDER REGULAR WITH K0(A) ? = ZZ 2 THE ?GR-?LTRATION ON MODULES 3 GENERAL CASE: GL DIMA ?N 4 GENERAL CASE: K0(A) ? = ZZ REFERENCES