Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.2/3817
Título: On a problem of M. Kambites regarding abundant semigroups
Autor: Araújo, João
Kinyon, Michael
Palavras-chave: Abundant semigroups
Adequate semigroups
Amiable semigroups
20M10
20M07
20M20
Data: 2012
Editora: http://www.tandfonline.com/doi/full/10.1080/00927872.2011.610072#.VRKIAk9ya1s
Citação: Araújo, João; Kinyon, Michael - On a problem of M. Kambites regarding abundant semigroups. "Communications in Algebra" [Em linha]. ISSN 0092-7872 (Print) 1532-4125 (Online). Vol. 40, nº 12 (2012), p. 1-8
Resumo: A 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.
Peer review: yes
URI: http://hdl.handle.net/10400.2/3817
DOI: 10.1080/00927872.2011.610072
ISSN: 0092-7872
1532-4125
Aparece nas colecções:Matemática e Estatística - Artigos em revistas internacionais / Papers in international journals

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