About: Refinement monoid

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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 said to be conical if x+y=0 implies that x=y=0, for any elements x,y of M.

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  • 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 said to be conical if x+y=0 implies that x=y=0, for any elements x,y of M. (en)
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  • 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 said to be conical if x+y=0 implies that x=y=0, for any elements x,y of M. (en)
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  • Refinement monoid (en)
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