User:Dfeuer/Definition:Cone Compatible with Closed Ringoid

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Definition

Let $\struct {R, *, \circ}$ be a closed ringoid.

Let $C$ be a cone compatible with $*$.

Then $C$ is compatible with $\struct {R, *, \circ}$ if and only if for each $x, y \in R$, the following holds:

$x, y \in C \implies x \circ y \in C$