Refinement Monoid
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. A join-semilattice with zero is a refinement monoid if and only if it is distributive.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. A join-semilattice with zero is a refinement monoid if and only if it is distributive.