Matemática e Estatística / Mathematics and Statistics
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Browsing Matemática e Estatística / Mathematics and Statistics by Subject "20M07"
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- On a problem of M. Kambites regarding abundant semigroupsPublication . Araújo, João; Kinyon, MichaelA semigroup is regular if it contains at least one idempotent in each -class and in each L-class. A regular semigroup is inverse if it satisfies either of the following equivalent conditions: (i) there is a unique idempotent in each -class and in each L-class, or (ii) the idempotents commute. Analogously, a semigroup is abundant if it contains at least one idempotent in each *-class and in each L*-class. An abundant semigroup is adequate if its idempotents commute. In adequate semigroups, there is a unique idempotent in each * and L*-class. M. Kambites raised the question of the converse: in a finite abundant semigroup such that there is a unique idempotent in each * and L*-class, must the idempotents commute? In this note, we provide a negative answer to this question.