Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.21/5011
Título: On the ranks of certain monoids of transformations that preserve a uniform partition
Autor: Fernandes, Vítor H.
Quinteiro, Teresa Maria de Araújo Melo
Palavras-chave: Equivalence-Preserving Transformations
Order-Preserving Transformations
Orientation-Preserving Transformations
Data: 1-Fev-2014
Editora: Taylor & Francis Inc
Citação: FERNANDES, Vítor H.; QUINTEIRO, Teresa Maria de Araújo Melo – On the ranks of certain monoids of transformations that preserve a uniform partition. Communications in Algebra. ISSN: 0092-7872. Vol. 42, nr. 2 (2014), pp. 615-636
Resumo: The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the cardinality of a least-size generating set. Semigroups of transformations that preserve or reverse the order or the orientation as well as semigroups of transformations preserving an equivalence relation have been widely studied over the past decades by many authors. The purpose of this article is to compute the ranks of the monoid 𝒪ℛ m×n of all orientation-preserving or orientation-reversing full transformations on a chain with mn elements that preserve a uniform m-partition and of its submonoids 𝒪𝒫 m×n of all orientation-preserving transformations and 𝒪𝒟 m×n of all order-preserving or order-reversing full transformations. These three monoids are natural extensions of 𝒪 m×n , the monoid of all order-preserving full transformations on a chain with mnelements that preserve a uniform m-partition.
Peer review: yes
URI: http://hdl.handle.net/10400.21/5011
DOI: 10.1080/00927872.2012.720322
ISSN: 0092-7872
Versão do Editor: http://www.tandfonline.com/doi/abs/10.1080/00927872.2012.720322#.U61RPoZJ6vw
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