Please use this identifier to cite or link to this item:

Author(s)Giraldes, E.
Smith, M. Paula Marques
Mitsch, H.
Natural partial order
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).
Publisher version
AccessOpen 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 PDFView/Open

Partilhe no FacebookPartilhe no TwitterPartilhe no DeliciousPartilhe no LinkedInPartilhe no DiggAdicionar ao Google BookmarksPartilhe no MySpacePartilhe no Orkut
Exporte no formato BibTex mendeley Exporte no formato Endnote Adicione ao seu ORCID