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B.2.4 Local orderings

For ls, ds, Ds and, if the weights are positive integers, also for ws and Ws, we have Loc 549#549 = 563#563, the localization of 549#549at the maximal ideal 564#564.

ls:
negative lexicographical ordering:
565#565.
ds:
negative degree reverse lexicographical ordering:
let 553#553 then 566#566 or
556#556 and 557#557
Ds:
negative degree lexicographical ordering:
let 553#553 then 566#566 or
556#556 and 558#558
ws:
(general) weighted reverse lexicographical ordering:
567#567 a nonzero integer, 568#568 any integer (including 0), is defined as ds but with 561#561
Ws:
(general) weighted lexicographical ordering:
569#569 a nonzero integer, 568#568 any integer (including 0), is defined as Ds but with 561#561


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