Lesson plan
Refinement monoid
In mathematics, a refinement monoid is a commutative monoid M such that for any elements a 0 , a 1 , b 0 , b 1 of M such that a 0 +a 1 =b 0 +b 1 , there are elements c 00 , c 01 , c 10 , c 11 of M such that a 0 =c 00 +c 01 , a 1 =c 10 +c 11 , b 0 =c 00 +c 10 , and b 1 =c 01 +c 11 . A commutative monoid M is said to be conical if x+y=0 implies that x=y=0, for any elements x,y of M.
Article summary
In mathematics, a refinement monoid is a commutative monoid M such that for any elements a 0 , a 1 , b 0 , b 1 of M such that a 0 +a 1 =b 0 +b 1 , there are elements c 00 , c 01 , c 10 , c 11 of M such that a 0 =c 00 +c 01 , a 1 =c 10 +c 11 , b 0 =c 00 +c 10 , and b 1 =c 01 +c 11 . A commutative monoid M is said to be conical if x+y=0 implies that x=y=0, for any elements x,y of M.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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