Weighted Expansions for Canonical Desingularization

Shreeram S. Abhyankar (auth.)9780387111957, 0-387-11195-6

Table of contents :
Notation….Pages 3-3
Semigroups….Pages 4-4
Strings….Pages 5-6
Semigroup strings with restrictions….Pages 7-9
Ordered semigroup strings with restrictions….Pages 10-10
Strings on rings….Pages 11-13
Indeterminate strings….Pages 14-20
Indeterminate strings with restrictions….Pages 21-25
Restricted degree and order for indeterminate strings….Pages 26-28
Indexing strings….Pages 29-30
Nets….Pages 31-32
Semigroup nets with restrictions….Pages 33-35
Ordered semigroup nets with restrictions….Pages 36-36
Nets on rings….Pages 37-38
Indeterminate nets….Pages 39-45
Indeterminate nets with restrictions….Pages 46-52
Restricted degree and order for indeterminate nets….Pages 53-56
Prechips….Pages 57-58
Isobars for prechips and Premonic polynomials….Pages 59-66
Substitutions….Pages 67-72
Substitutions with restrictions….Pages 73-81
Coordinate nets and Monic polynomials….Pages 82-84
Graded ring of a ring at an ideal….Pages 85-87
Graded ring of a ring….Pages 88-89
Graded rings at strings and nets and the notions of separatedness and regularity for strings and nets….Pages 90-103
Inner products and further notions of separatedness and regularity for strings….Pages 104-108
Inner products and further notions of separatedness and regularity for nets….Pages 109-112
Weighted isobars and weighted initial forms….Pages 113-125
Initial forms for regular strings….Pages 126-149
Initial forms for regular strings and nets….Pages 150-160
Protochips and parachips….Pages 161-161
N-support of an indexing string for 2≤N≤6….Pages 162-162
Prescales….Pages 163-164
Derived prescales….Pages 165-166
Supports of prescales….Pages 167-167
Protoscales….Pages 168-169
Inner products for protoscales….Pages 170-170
Scales and isobars….Pages 171-175
Properties of derived prescales….Pages 176-202
Isobars for derived scales….Pages 203-204
Isobars and initial forms for scales….Pages 205-213
Initial forms for scales and regular nets….Pages 214-219
Isobars for protochips….Pages 220-220
Initial forms for protochips and monic polynomials….Pages 221-224