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
- Definition:Naturally Ordered Semigroup
- Definition:Positively Totally Ordered Semigroup
- Definition:Right Naturally Totally Ordered Semigroup
- Definition:Naturally Totally Ordered Semigroup
Sources
- 1978: M. Satyanarayana: Naturally totally ordered semigroups (Pacific J. Math. Vol. 77, no. 1: pp. 249 – 254)