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

TitleF-monoids
Author(s)Giraldes, E.
Smith, M. Paula Marques
Mitsch, H.
KeywordsE-inversive
E-unitary
Group-congruence
Natural partial order
Monoid
E-inversive E-unitary
Issue date2007
PublisherTaylor & Francis
JournalCommunications 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).
TypeArticle
URIhttp://hdl.handle.net/1822/11065
DOI10.1080/00927870701326494
ISSN0092-7872
1532-4125
Publisher versionhttp://www.informaworld.com/smpp/content~db=all~content=a781318841~frm=abslink
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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