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Equivalence Systems Derived From Partial Orders by Gerhard Behrendt is a Mathematics article available to read on EtoBox.

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Let R be a binary relation on a set X, and let S(R) = -e X\*x|xRy}. We define equivalence relations R^ and R, on S(R) by (x., ,x 2 )R i (y 1 ,y 2 ) if and only if x ± = (for i=1,2). We show that if R is a partial order then (X,R) is uniquely determined up to isomorphism or dual isomorphism by the derived equivalence system (S(R) ,R 2 })» and tilat it has the same automorphism group. Furthermore, every group is isomorphic to the automorphism group of an equivalence system derived from a partial order. We give criteria to deto the derived system of a partial order, or of an equivalence relation.

Who reads Equivalence Systems Derived From Partial Orders?

Author

Gerhard Behrendt

Published

1988

Language

EN

Field

Mathematics (Physical Sciences)