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单词 CompletelySimpleSemigroup
释义

completely simple semigroup


Let S be a semigroup. An idempotentPlanetmathPlanetmath eS is primitive if for every other idempotent fS, ef=fe=f0e=f

A semigroup S (without zero) is completely if it is simple and contains a primitive idempotent.

A semigroup S is completely 0-simple if it is 0-simple (http://planetmath.org/SimpleSemigroup) and contains a primitive idempotent.

Completely simple and completely 0-simple semigroups maybe characterised by the Rees Theorem ([Ho95], Theorem 3.2.3).

Note:

A semigroup (without zero) is completely simple if and only if it is regularPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath and weakly cancellative.

A simple semigroup (without zero) is completely simple if and only if it is completely regularPlanetmathPlanetmath.

A 0-simple semigroup is completely 0-simple if and only if it is group-bound.

References

  • Ho95 Howie, John M. Fundamentals of Semigroup Theory. Oxford University Press, 1995.
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更新时间:2025/5/4 14:32:32