Definition:Positively Totally Ordered Semigroup

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Definition

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


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

$(1): \forall a, b \in S: a \preceq a \circ b$

and

$(2): \forall a, b \in S: b \preceq a \circ b$


Also see


Sources