Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/11065

 Title: F-monoids Author(s): Giraldes, E.Smith, M. Paula MarquesMitsch, H. Keywords: E-inversiveE-unitaryGroup-congruenceNatural partial orderMonoidE-inversive E-unitary Issue date: 2007 Publisher: Taylor & Francis Journal: Communications in Algebra Citation: “Communications in Algebra”. ISSN 0092-7872. 35:8 (2007) 2552-2567. Abstract(s): A semigroup $S$ is called $F-monoid$ if $S$ has an identity and if there exists a group congruence $\rho$ on $S$ such that each $\rho$-class of $S$ contains a greatest element with respect to the natural partial order of $S$ (see Mitsch, 1986). Generalizing results given in Giraldes et al. (2004) and specializing some of Giraldes et al. (Submitted) ﬁve characterizations of such monoids $S$ are provided. Three unary operations $\star$, $\circ$ and $-$ on $S$ deﬁned by means of the greatest elements in the different $\rho$-classes of $S$ are studied. Using their properties, a charaterization of $F$-monoids $S$ by their regular part $S^\circ=\{a^\circ:a\in S\}$ and the associates of elements in $S^\circ$ is given. Under the hypothesis that $S^\star=\{a^\star:a\in S\}$ is a subsemigroup it is shown that $S$ is regular, whence of a known structure (see Giraldes et al., 2004). Type: Article URI: http://hdl.handle.net/1822/11065 DOI: 10.1080/00927870701326494 ISSN: 0092-78721532-4125 Publisher version: http://www.informaworld.com/smpp/content~db=all~content=a781318841~frm=abslink Peer-Reviewed: yes Access: Open access Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

Files in This Item:
File Description SizeFormat
monoids.pdfDocumento principal203,86 kBAdobe PDF