Definition:Left Naturally Totally Ordered Semigroup

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Definition

Let $\struct {S, \circ, \preceq}$ be a positively totally ordered semigroup.


Then $\struct {S, \circ, \preceq}$ is a left naturally totally ordered semigroup if and only if:

$a \prec b \implies \exists x \in S: b = x \circ a$


Also see


Sources

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