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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 551#551 = 565#565, the localization of 551#551at the maximal ideal 566#566.

ls:
negative lexicographical ordering:
567#567.
ds:
negative degree reverse lexicographical ordering:
let 555#555 then 568#568 or
558#558 and 559#559
Ds:
negative degree lexicographical ordering:
let 555#555 then 568#568 or
558#558 and 560#560
ws:
(general) weighted reverse lexicographical ordering:
569#569 a nonzero integer, 570#570 any integer (including 0), is defined as ds but with 563#563
Ws:
(general) weighted lexicographical ordering:
571#571 a nonzero integer, 570#570 any integer (including 0), is defined as Ds but with 563#563


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