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Soc."],"published-print":{"date-parts":[[2006,6]]},"abstract":"<jats:p>We consider the symmetric inverse monoid \u2110<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>of an<jats:italic>n<\/jats:italic>-element chain and its inverse submonoids \uf10f\uf10e\u2110<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, \uf10f\uf10e\uf103\u2110<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, \uf10f\uf10e\uf10f\u2110<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>and \uf10f\uf10e\u2118\u2110<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>of all order-preserving, order-preserving or order-reversing, orientation-preserving and orientation-preserving or orientation-reversing transformations, respectively, and give descriptions of their Abelian kernels relative to decidable pseudovarieties of Abelian groups.<\/jats:p>","DOI":"10.1017\/s0004972700035413","type":"journal-article","created":{"date-parts":[[2009,4,17]],"date-time":"2009-04-17T14:17:10Z","timestamp":1239977830000},"page":"375-404","source":"Crossref","is-referenced-by-count":2,"title":["Relative Abelian kernels of some classes of transformation monoids"],"prefix":"10.1017","volume":"73","author":[{"given":"E.","family":"Cordeiro","sequence":"first","affiliation":[]},{"given":"M.","family":"Delgado","sequence":"additional","affiliation":[]},{"given":"V.H.","family":"Fernandes","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,4,17]]},"reference":[{"key":"S0004972700035413_ref022","first-page":"191","article-title":"The defining relations of certain semigroups of partial transformations of a finite set","volume":"218","author":"Popova","year":"1961","journal-title":"Leningradskij gosudarstvennyj pedagogicheskij institut imeni A. 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