Ring theory and algebraic geometry: proceedings of the fifth international conference

EEn......Page 1
Ring Theory and Algebraic Geometry......Page 2
Back Cover......Page 3
Copyright Info......Page 6
Preface......Page 12
TOC......Page 13
Contributors......Page 15
Conference Participants......Page 17
1 INTRODUCTION......Page 24
2 SEPARABLE FUNCTORS AND FROBENIUS PAIRS OF FUNCTORS......Page 26
3 ENTWINED MODULES AND DOI- HOPF MODULES......Page 30
4 THE FUNCTOR FORGETTING THE COACTION......Page 32
5 THE FUNCTOR FORGETTING THE A- ACTION......Page 42
6 THE SMASH PRODUCT......Page 50
REFERENCES......Page 53
1 INTRODUCTION......Page 55
2 ADMISSIBLE ORDERS IN MONOIDEALS AND STABLE SUBSETS......Page 56
3 PBW ALGEBRAS, QUANTUM RELATIONS AND FILTRATIONS......Page 59
4 CONSEQUENCES AND EXAMPLES......Page 66
5 GROBNER BASES FOR MODULES......Page 70
6 HOMOGENEOUS GROBNER BASES......Page 73
7 THE GELFAND-KIRILLOV DIMENSION......Page 75
References......Page 77
1 INTRODUCTION......Page 80
2.1 Obtaining laws of families of filiform Lie algebras......Page 83
2.2 Low-dimensional filiform Lie algebras......Page 84
2.3 /c-abelian filiform Lie algebras......Page 86
3.1 p- filiform Lie algebras with p > n — 3......Page 87
3.3 p-filiform Lie algebras with n — 6 < p < n — 5......Page 89
4 LIE ALGEBRAS WITH SMALL NILINDEX......Page 90
4.1 Metabelian Lie algebras......Page 91
5 NATURALLY GRADED NILPOTENT LIE ALGEBRAS......Page 93
5.1 Naturally Graded filiform and Quasi- filiform Lie Algebras......Page 94
5.2 Naturally Graded 3-filiform Lie Algebras......Page 96
6 LENGTH OF NILPOTENT LIE ALGEBRAS......Page 98
6.2 Filiform Lie Algebra of maximum Length......Page 99
6.3 Quasi- filiform Lie algebras of length greater than their nilindex......Page 101
7 SYMBOLIC CALCULUS ON LIE ALGEBRAS......Page 102
REFERENCES......Page 103
1 PREVIOUS RESULTS ON //-TRIPLES......Page 108
2 PREVIOUS RESULTS ON JORDAN //"-PAIRS......Page 110
3 MAIN RESULTS......Page 112
REFERENCES......Page 115
I INTRODUCTION......Page 116
2 SEMIGROUP AND GENERATORS OF TORIC GEOMETRY......Page 117
3 ABELIAN GROUPS AND LATTICES......Page 118
4 SEMIGROUP IDEALS AND ALGEBRAS......Page 119
5 CONES AND FANS......Page 121
6 AFFINE AND PROJECTIVE TORIC VARIETIES......Page 122
7 POLYTOPES, SIMPLICIAL AND CELLULAR COMPLEXES......Page 124
8 MULTINUMERICAL SEMIGROUPS......Page 129
9 APPLICATIONS......Page 130
REFERENCES......Page 132
1 INTRODUCTION......Page 134
2 LINEAR DYNAMICAL SYSTEMS OVER COMMUTATIVE RINGS: THE FEEDBACK GROUP......Page 135
3 CANONICAL FORM FOR SYSTEMS OVER FIELDS......Page 137
4 DEALING WITH THE LOCAL CASE......Page 142
REFERENCES......Page 151
I INTRODUCTION......Page 153
2.1 Janet modules......Page 154
3 COMPLETELY INTEGRABLE SYSTEMS. JANET BASES......Page 155
4.1 Homogeneous systems......Page 156
4.2 Non-homogeneous systems......Page 160
REFERENCES......Page 162
1 INTRODUCTION......Page 166
2 PRELIMINARIES......Page 167
3 THE PICARD GROUP......Page 169
3.1 Definitions and properties......Page 170
3.2 The Aut-Pic property......Page 171
4.1 Definitions and properties......Page 175
4.2 Torsioness in the Brauer group......Page 179
4.3 Subgroups of the Brauer group......Page 184
REFERENCES......Page 188
1 INTRODUCTION......Page 191
2 MONOIDAL CATEGORIES......Page 192
3 GENERAL PROPERTIES OF MULTIPLICATION OBJECTS......Page 195
4 ENDOMORPHISMS OF MULTIPLICATION OBJECTS......Page 200
REFERENCES......Page 203
1 SEMILOCAL RINGS AND MODULES WHOSE ENDOMORPHISM RING IS SEMILOCAL......Page 205
2 K0 OF A SEMILOCAL RING......Page 208
3 UNISERIAL MODULES......Page 213
4 HOMOGENEOUS SEMILOCAL RINGS AND MODULES WHOSE ENDOMORPHISM RING IS HOMOGENEOUS SEMILOCAL......Page 216
REFERENCES......Page 218
1 INTRODUCTION......Page 220
2.1 Maximal ideals......Page 221
2.3 Normalization of unimodular vectors......Page 223
3 APPLICATIONS TO K-THEORY......Page 224
REFERENCES......Page 226
1 INTRODUCTION......Page 228
2 PERFECT RINGS AND PSEUDO-FROBENIUS RINGS......Page 230
3 RINGS WHOSE CLASS OF FINITE-DIMENSIONAL MODULES IS SOCLE-FINE......Page 232
4 RADICAL-FINE CHARACTERIZATION OF RINGS......Page 235
REFERENCES......Page 237
1 PRELIMINARY RESULTS......Page 239
2 IDEMPOTENTS......Page 241
3 RELATIONS WITH OTHER CLASSES OF ALGEBRAS......Page 243
4 BERNSTEIN PROBLEM......Page 245
5 AUTOMORPHISMS AND DERIVATIONS......Page 246
6 SOME OTHER ASPECTS......Page 248
REFERENCES......Page 252
1 INTRODUCTION......Page 256
2 HOMOGENIZATION OF DIFFERENTIAL OPERATORS......Page 260
3 COMPUTATION OF THE BERNSTEIN POLYNOMIAL......Page 262
REFERENCES......Page 264
I INTRODUCTION......Page 266
3 COHEN-MACAULAY CONDITION......Page 267
4 RESULTS......Page 268
REFERENCES......Page 270
1 INTRODUCTION......Page 272
2 DIVISORS......Page 275
3 DIVISOR CLASS GROUP......Page 281
4 THE EXPECTED CANONICAL MODULE......Page 284
5 THE FUNDAMENTAL DIVISOR......Page 287
6 COHEN-MACAULAY DIVISORS AND REDUCTION NUMBERS......Page 295
7 VANISHING OF COHOMOLOGY......Page 296
REFERENCES......Page 301
1 INTRODUCTION......Page 304
2 IRREDUCIBLE MONOMIAL CURVES......Page 305
3 REDUCED MONOMIAL CURVES......Page 306
4 MONOMIAL CURVES AND EULER VECTOR FIELDS......Page 307
5 ALGORITHM......Page 308
REFERENCES......Page 310
1 INTRODUCTION......Page 312
2 GENERALITIES......Page 313
3 INVOLUTIVE INVARIANTS OF THE SECOND KIND......Page 314
4 AMITSUR COHOMOLOGY......Page 317
REFERENCES......Page 324
1 INTRODUCTION......Page 326
2 DEFINITIONS......Page 327
3 FINITENESS OF THE NUMBER OF SLOPES......Page 329
4 A WAY OF COMPUTING AL M......Page 331
6 ABOUT THE COMPUTATIONS IN V.......Page 332
7.1 Slopes of O [ l / f ] / O .......Page 335
7.2 Looking for slopes in a syzygy module......Page 336
7.3 Slopes and direct sums of ideals......Page 337
REFERENCES......Page 338
1 INTRODUCTION......Page 340
2 SOME BACKGROUND ON CLOSED CATEGORIESo......Page 341
3 MONOIDS WITH INVOLUTION......Page 345
4 THE INVOLUTIVE BRAUER GROUP......Page 346
5 FUNCTORIAL BEHAVIOUR......Page 349
REFERENCES......Page 352