Chaos Organization and Disaster Management (Public Administration and Public Policy)

Ring Theory and Algebraic Geometry......Page 1
Back Cover......Page 2
Copyright Info......Page 5
Preface......Page 11
TOC......Page 12
Contributors......Page 14
Conference Participants......Page 16
1 INTRODUCTION......Page 23
2 SEPARABLE FUNCTORS AND FROBENIUS PAIRS OF FUNCTORS......Page 25
3 ENTWINED MODULES AND DOI- HOPF MODULES......Page 29
4 THE FUNCTOR FORGETTING THE COACTION......Page 31
5 THE FUNCTOR FORGETTING THE A- ACTION......Page 41
6 THE SMASH PRODUCT......Page 49
REFERENCES......Page 52
1 INTRODUCTION......Page 54
2 ADMISSIBLE ORDERS IN MONOIDEALS AND STABLE SUBSETS......Page 55
3 PBW ALGEBRAS, QUANTUM RELATIONS AND FILTRATIONS......Page 58
4 CONSEQUENCES AND EXAMPLES......Page 65
5 GROBNER BASES FOR MODULES......Page 69
6 HOMOGENEOUS GROBNER BASES......Page 72
7 THE GELFAND-KIRILLOV DIMENSION......Page 74
References......Page 76
1 INTRODUCTION......Page 79
2.1 Obtaining laws of families of filiform Lie algebras......Page 82
2.2 Low-dimensional filiform Lie algebras......Page 83
2.3 /c-abelian filiform Lie algebras......Page 85
3.1 p- filiform Lie algebras with p > n — 3......Page 86
3.3 p-filiform Lie algebras with n — 6 < p < n — 5......Page 88
4 LIE ALGEBRAS WITH SMALL NILINDEX......Page 89
4.1 Metabelian Lie algebras......Page 90
5 NATURALLY GRADED NILPOTENT LIE ALGEBRAS......Page 92
5.1 Naturally Graded filiform and Quasi- filiform Lie Algebras......Page 93
5.2 Naturally Graded 3-filiform Lie Algebras......Page 95
6 LENGTH OF NILPOTENT LIE ALGEBRAS......Page 97
6.2 Filiform Lie Algebra of maximum Length......Page 98
6.3 Quasi- filiform Lie algebras of length greater than their nilindex......Page 100
7 SYMBOLIC CALCULUS ON LIE ALGEBRAS......Page 101
REFERENCES......Page 102
1 PREVIOUS RESULTS ON //-TRIPLES......Page 107
2 PREVIOUS RESULTS ON JORDAN //"-PAIRS......Page 109
3 MAIN RESULTS......Page 111
REFERENCES......Page 114
I INTRODUCTION......Page 115
2 SEMIGROUP AND GENERATORS OF TORIC GEOMETRY......Page 116
3 ABELIAN GROUPS AND LATTICES......Page 117
4 SEMIGROUP IDEALS AND ALGEBRAS......Page 118
5 CONES AND FANS......Page 120
6 AFFINE AND PROJECTIVE TORIC VARIETIES......Page 121
7 POLYTOPES, SIMPLICIAL AND CELLULAR COMPLEXES......Page 123
8 MULTINUMERICAL SEMIGROUPS......Page 128
9 APPLICATIONS......Page 129
REFERENCES......Page 131
1 INTRODUCTION......Page 133
2 LINEAR DYNAMICAL SYSTEMS OVER COMMUTATIVE RINGS: THE FEEDBACK GROUP......Page 134
3 CANONICAL FORM FOR SYSTEMS OVER FIELDS......Page 136
4 DEALING WITH THE LOCAL CASE......Page 141
REFERENCES......Page 150
I INTRODUCTION......Page 152
2.1 Janet modules......Page 153
3 COMPLETELY INTEGRABLE SYSTEMS. JANET BASES......Page 154
4.1 Homogeneous systems......Page 155
4.2 Non-homogeneous systems......Page 159
REFERENCES......Page 161
1 INTRODUCTION......Page 165
2 PRELIMINARIES......Page 166
3 THE PICARD GROUP......Page 168
3.1 Definitions and properties......Page 169
3.2 The Aut-Pic property......Page 170
4.1 Definitions and properties......Page 174
4.2 Torsioness in the Brauer group......Page 178
4.3 Subgroups of the Brauer group......Page 183
REFERENCES......Page 187
1 INTRODUCTION......Page 190
2 MONOIDAL CATEGORIES......Page 191
3 GENERAL PROPERTIES OF MULTIPLICATION OBJECTS......Page 194
4 ENDOMORPHISMS OF MULTIPLICATION OBJECTS......Page 199
REFERENCES......Page 202
1 SEMILOCAL RINGS AND MODULES WHOSE ENDOMORPHISM RING IS SEMILOCAL......Page 204
2 K0 OF A SEMILOCAL RING......Page 207
3 UNISERIAL MODULES......Page 212
4 HOMOGENEOUS SEMILOCAL RINGS AND MODULES WHOSE ENDOMORPHISM RING IS HOMOGENEOUS SEMILOCAL......Page 215
REFERENCES......Page 217
1 INTRODUCTION......Page 219
2.1 Maximal ideals......Page 220
2.3 Normalization of unimodular vectors......Page 222
3 APPLICATIONS TO K-THEORY......Page 223
REFERENCES......Page 225
1 INTRODUCTION......Page 227
2 PERFECT RINGS AND PSEUDO-FROBENIUS RINGS......Page 229
3 RINGS WHOSE CLASS OF FINITE-DIMENSIONAL MODULES IS SOCLE-FINE......Page 231
4 RADICAL-FINE CHARACTERIZATION OF RINGS......Page 234
REFERENCES......Page 236
1 PRELIMINARY RESULTS......Page 238
2 IDEMPOTENTS......Page 240
3 RELATIONS WITH OTHER CLASSES OF ALGEBRAS......Page 242
4 BERNSTEIN PROBLEM......Page 244
5 AUTOMORPHISMS AND DERIVATIONS......Page 245
6 SOME OTHER ASPECTS......Page 247
REFERENCES......Page 251
1 INTRODUCTION......Page 255
2 HOMOGENIZATION OF DIFFERENTIAL OPERATORS......Page 259
3 COMPUTATION OF THE BERNSTEIN POLYNOMIAL......Page 261
REFERENCES......Page 263
I INTRODUCTION......Page 265
3 COHEN-MACAULAY CONDITION......Page 266
4 RESULTS......Page 267
REFERENCES......Page 269
1 INTRODUCTION......Page 271
2 DIVISORS......Page 274
3 DIVISOR CLASS GROUP......Page 280
4 THE EXPECTED CANONICAL MODULE......Page 283
5 THE FUNDAMENTAL DIVISOR......Page 286
6 COHEN-MACAULAY DIVISORS AND REDUCTION NUMBERS......Page 294
7 VANISHING OF COHOMOLOGY......Page 295
REFERENCES......Page 300
1 INTRODUCTION......Page 303
2 IRREDUCIBLE MONOMIAL CURVES......Page 304
3 REDUCED MONOMIAL CURVES......Page 305
4 MONOMIAL CURVES AND EULER VECTOR FIELDS......Page 306
5 ALGORITHM......Page 307
REFERENCES......Page 309
1 INTRODUCTION......Page 311
2 GENERALITIES......Page 312
3 INVOLUTIVE INVARIANTS OF THE SECOND KIND......Page 313
4 AMITSUR COHOMOLOGY......Page 316
REFERENCES......Page 323
1 INTRODUCTION......Page 325
2 DEFINITIONS......Page 326
3 FINITENESS OF THE NUMBER OF SLOPES......Page 328
4 A WAY OF COMPUTING AL M......Page 330
6 ABOUT THE COMPUTATIONS IN V.......Page 331
7.1 Slopes of O [ l / f ] / O .......Page 334
7.2 Looking for slopes in a syzygy module......Page 335
7.3 Slopes and direct sums of ideals......Page 336
REFERENCES......Page 337
1 INTRODUCTION......Page 339
2 SOME BACKGROUND ON CLOSED CATEGORIESo......Page 340
3 MONOIDS WITH INVOLUTION......Page 344
4 THE INVOLUTIVE BRAUER GROUP......Page 345
5 FUNCTORIAL BEHAVIOUR......Page 348
REFERENCES......Page 351