Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/16882

TitleInverse semigroups generated by nilpotent transformations
Author(s)Howie, John M.
Smith, M. Paula Marques
KeywordsInverse semigroup
Nilpotents
Transformations
Congruences
Issue date1984
PublisherCambridge University Press
JournalProceedings of the Royal Society of Edinburgh
Abstract(s)Let $X$ be a set with infinite cardinality $m$ and let $B$ be the Baer-Levi semigroup, consisting of all one-one mappings $a:X\rightarrow X$ for which $∣X\Xα∣ = m$. Let $K_m=<B^{-1}B>$, the inverse subsemigroup of the symmetric inverse semigroup $\mathcal T(X)$ generated by all products $\beta^{−1}\gamma$, with $\beta,1\gamma\in B$. Then $K_m = <N_2>$, where $N_2$ is the subset of $\mathcal T(X)$ consisting of all nilpotent elements of index 2. Moreover, $K_m$ has 2-nilpotent-depth 3, in the sense that $N_2\cup N_2^2\subset K_m = N_2\cup N_2^2\cup N_2^3$. Let $P_m$ be the ideal $\{\alpha\in K_m: ∣dom \alpha∣<m\}$ in $K_m$ and let $L_m$ be the Rees quotient $K_m/P_m$. Then $L_m$ is a 0-bisimple, 2-nilpotent-generated inverse semigroup with 2-nilpotent-depth 3. The minimum non-trivial homomorphic image $L_m^*$ of $L_m$ also has these properties and is congruence-free.
TypeArticle
URIhttp://hdl.handle.net/1822/16882
DOI10.1017/S0308210500026032
ISSN0308-2105
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

Files in This Item:
File Description SizeFormat 
Inv_sgps_nilpo_transf.pdf2,68 MBAdobe 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