In mathematics, a refinement monoid is a commutative monoid M such that for any elements a0, a1, b0, b1 of M such that a0+a1=b0+b1, there are elements c00, c01, c10, c11 of M such that a0=c00+c01, a1=c10+c11, b0=c00+c10, and b1=c01+c11.
A commutative monoid M is conical, if x+y=0 implies that x=y=0, for any elements x,y of M.
Read more about Refinement Monoid: Basic Examples, Vaught Measures On Boolean Algebras, Nonstable K-theory of Von Neumann Regular Rings
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