Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/2144

 Title: On semidirectly closed pseudovarieties of aperiodic semigroups Author(s): Teixeira, M. L. Keywords: SemigroupSemigrupoidGraphSemidirect productPseudovarietySemidirectly closedImplicit operationPseudoidentity20M0520M0720M35 Issue date: 2001 Publisher: Elsevier Journal: Journal of Pure and Applied Algebra Citation: "Journal of pure and applied algebra". ISSN 0022-4049. 160 (2001) 229-248. Abstract(s): The aim of this work is to study the unknown intervals of the lattice of aperiodic pseu\-do\-va\-rie\-ties which are semidirectly closed and answer questions proposed by J.~Almeida in his book Finite Semigroups and Universal Algebra". The main results state that the intervals $[\mathbf{V}^*(B_2),\mathbf{ER}\cap\mathbf{LR}]$ and $[\mathbf{V}^*(B^1_2),\mathbf{ER}\cap\mathbf{A}]$ are not trivial, and that both contain a chain isomorphic to the chain of real numbers. These results are a consequence of the study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup $B_2$. Type: Article URI: http://hdl.handle.net/1822/2144 DOI: 10.1016/S0022-4049(00)00073-6 ISSN: 0022-4049 Peer-Reviewed: yes Access: Open access Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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