{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:29:05Z","timestamp":1759073345172},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,6]]},"abstract":"<jats:p> In linear algebraic monoid theory, the Renner monoids play the role of the Weyl groups in linear algebraic group theory. It is well known that Weyl groups are Coxeter groups, and that we can associate a Hecke algebra and an Artin\u2013Tits group to each Coxeter group. The question of the existence of a Hecke algebra associated with each Renner monoid has been positively answered. In this paper we discuss the question of the existence of an equivalent of the Artin\u2013Tits groups in the framework of Renner monoids. We consider the seminal case of the rook monoid and introduce a new length function. <\/jats:p>","DOI":"10.1142\/s0218196708004603","type":"journal-article","created":{"date-parts":[[2008,6,24]],"date-time":"2008-06-24T05:38:40Z","timestamp":1214285920000},"page":"779-802","source":"Crossref","is-referenced-by-count":3,"title":["THE BRAID ROOK MONOID"],"prefix":"10.1142","volume":"18","author":[{"given":"EDDY","family":"GODELLE","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Nicolas Oresme, UMR 6139 CNRS, Universit\u00e9 de Caen BP 5186, 14032 Caen, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02950718"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1080\/00927870008827165"},{"key":"rf4","series-title":"Annals of Mathematics Studies","volume-title":"Braids, Links, and Mapping Class Groups","volume":"82","author":"Birman J.","year":"1974"},{"key":"rf5","volume-title":"\u00e9l\u00e9ments de math\u00e9matique. 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