Post #1368987
2026-03-24 05:18 UTC
@soaproot No, it's the same thing. Wikipedia just uses multiplicative notation and talks about (X_1)^(m_r) * … * (X_m)^(m_r) where X_1, …, X_r are formal symbols and (m_1, …, m_r) ∈ ℕ^r, instead of (m_1, …, m_r) directly. I just decided to strip away the multiplicative notation to make the post more widely accessible.
At first they leave the conditions »total order« and »the neutral element is minimal« from my original post away, but they add them in »Definition, details and variants« and mention the relation with well-ordering.
Replies (1)
-
@soaproot@sfba.social 2026-03-24 05:28
@jdw I wasn't worried about the additive versus multiplicative notation, I was worried about not noticing "Classically, every monomial ordering is a well-ordering " or Hilbert's basis theorem on the Wikipedia page. But when I re-read your post about the "neutral element is minimal" condition, I think I better see how they line up (while still not wanting to overstate my understanding of all the details).