Weighted Expansions for Canonical Desingularization

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