Category:Definitions/Inductive Semigroups
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This category contains definitions related to Inductive Semigroups.
Related results can be found in Category:Inductive Semigroups.
Let $\struct {S, \circ}$ be a semigroup.
Let there exist $\alpha, \beta \in S$ such that the only subset of $S$ containing both $\alpha$ and $x \circ \beta$ whenever it contains $x$ is $S$ itself.
That is:
- $\exists \alpha, \beta \in S: \forall A \subseteq S: \paren {\alpha \in A \land \paren {\forall x \in A: x \circ \beta \in A} } \implies A = S$
Then $\struct {S, \circ}$ is an inductive semigroup.
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Pages in category "Definitions/Inductive Semigroups"
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