{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T01:37:24Z","timestamp":1649209044809},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algebra Colloq."],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:p> Suppose V is an infinite-dimensional vector space and let T(V) denote the semigroup (under composition) of all linear transformations of V. In this paper, we study the semigroup OM(p,q) consisting of all \u03b1 \u2208 T(V) for which dim ker \u03b1 \u2265 q and the semigroup OE(p,q) of all \u03b1 \u2208 T(V) for which codim ran \u03b1 \u2265 q, where dim V = p \u2265 q \u2265 \u2135<jats:sub>0<\/jats:sub>. It is not difficult to see that OM(p,q) and OE(p,q) are a right ideal and a left ideal of T(V), respectively, and using these facts, we show that they belong to the class of all semigroups whose sets of bi-ideals and quasi-ideals coincide. Also, we describe Green's relations and the two-sided ideals of each semigroup, and determine its maximal regular subsemigroup. Finally, we determine some maximal right cancellative subsemigroups of OE(p,q). <\/jats:p>","DOI":"10.1142\/s1005386710000131","type":"journal-article","created":{"date-parts":[[2014,2,5]],"date-time":"2014-02-05T01:13:38Z","timestamp":1391562818000},"page":"109-120","source":"Crossref","is-referenced-by-count":3,"title":["The Ideal Structure of Semigroups of Linear Transformations with Lower Bounds on Their Nullity or Defect"],"prefix":"10.1142","volume":"17","author":[{"given":"Suzana","family":"Mendes-Gon\u00e7alves","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica, Universidade do Minho, 4710 Braga, Portugal"}]},{"given":"R. P.","family":"Sullivan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of Western Australia, Nedlands 6009, Australia"}]}],"member":"219","published-online":{"date-parts":[[2012,5,3]]},"reference":[{"key":"rf1","series-title":"Mathematical Surveys","volume-title":"The Algebraic Theory of Semigroups, Vols. 1 and 2","volume":"7","author":"Cli A. H.","year":"1967"},{"key":"rf2","volume-title":"An Introduction to Semigroup Theory","author":"Howie J. M.","year":"1976"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-7053-6"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120013335"},{"key":"rf5","first-page":"405","volume":"12","author":"Kemprasit Y.","journal-title":"Pure Math. Appl."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1080\/00927870500346271"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1080\/00927870802622932"},{"key":"rf9","first-page":"237","volume":"43","author":"Namnak C.","journal-title":"Kyungpook Math. J."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500013688"}],"container-title":["Algebra Colloquium"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1005386710000131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:13:27Z","timestamp":1565111607000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1005386710000131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,5,3]]},"published-print":{"date-parts":[[2010,3]]}},"alternative-id":["10.1142\/S1005386710000131"],"URL":"https:\/\/doi.org\/10.1142\/s1005386710000131","relation":{},"ISSN":["1005-3867","0219-1733"],"issn-type":[{"value":"1005-3867","type":"print"},{"value":"0219-1733","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3]]}}}