{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T11:38:11Z","timestamp":1648553891384},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2013,8]]},"abstract":"<jats:p> In this paper we continue the investigation on the algebraic structure of a finite semigroup S that is determined by its associated upper non-nilpotent graph [Formula: see text]. The vertices of this graph are the elements of S and two vertices are adjacent if they generate a semigroup that is not nilpotent (in the sense of Mal'cev). We introduce a class of semigroups in which the Mal'cev nilpotent property lifts through ideal chains. We call this the class of pseudo-nilpotent semigroups. The definition is such that the global information that a semigroup is not nilpotent induces local information, i.e. some two-generated subsemigroups are not nilpotent. It turns out that a finite monoid (in particular, a finite group) is pseudo-nilpotent if and only if it is nilpotent. Our main result is a description of pseudo-nilpotent finite semigroups S in terms of their associated graph [Formula: see text]. In particular, S has a largest nilpotent ideal, say K, and S\/K is a 0-disjoint union of its connected components (adjoined with a zero) with at least two elements. <\/jats:p>","DOI":"10.1142\/s0219498812502210","type":"journal-article","created":{"date-parts":[[2012,10,19]],"date-time":"2012-10-19T08:24:15Z","timestamp":1350635055000},"page":"1250221","source":"Crossref","is-referenced-by-count":1,"title":["A DESCRIPTION OF A CLASS OF FINITE SEMIGROUPS THAT ARE NEAR TO BEING MAL'CEV NILPOTENT"],"prefix":"10.1142","volume":"12","author":[{"given":"E.","family":"JESPERS","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium"}]},{"given":"M. H.","family":"SHAHZAMANIAN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium"}]}],"member":"219","published-online":{"date-parts":[[2013,5,7]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1080\/00927870903386460"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/007.1"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1994.1322"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1999-036-2"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706002913"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-012-9389-z"},{"key":"rf8","first-page":"107","volume":"4","author":"Mal'cev A. I.","year":"1953","journal-title":"Uc. Zap. Ivanovsk. Ped. Inst."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1963.0110"},{"key":"rf10","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","volume-title":"Semigroup Algebras","volume":"138","author":"Okninski J.","year":"1991"}],"container-title":["Journal of Algebra and Its Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219498812502210","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:00:31Z","timestamp":1565125231000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219498812502210"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,7]]},"references-count":10,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2013,5,7]]},"published-print":{"date-parts":[[2013,8]]}},"alternative-id":["10.1142\/S0219498812502210"],"URL":"https:\/\/doi.org\/10.1142\/s0219498812502210","relation":{},"ISSN":["0219-4988","1793-6829"],"issn-type":[{"value":"0219-4988","type":"print"},{"value":"1793-6829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,7]]}}}