{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T13:30:39Z","timestamp":1773235839039,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2013,2]]},"abstract":"<jats:p> Let [Formula: see text] be the monoid generated by [Formula: see text] We introduce the homogeneous catenary degree of [Formula: see text] as the smallest N \u2208 \u2115 with the following property: for each [Formula: see text] and any two factorizations u, v of a, there exist factorizations u = w<jats:sub>1<\/jats:sub>,\u2026,w<jats:sub>t<\/jats:sub> = v of a such that, for every k, d (w<jats:sub>k<\/jats:sub>,w<jats:sub>k+1<\/jats:sub>) \u2264 N, where d is the usual distance between factorizations, and the length of w<jats:sub>k<\/jats:sub>, |w<jats:sub>k<\/jats:sub>|, is less than or equal to max{|u|, |v|}. We prove that the homogeneous catenary degree of [Formula: see text] improves the monotone catenary degree as upper bound for the ordinary catenary degree, and we show that it can be effectively computed. We also prove that for half-factorial monoids, the tame degree and the \u03c9-primality coincide, and that all possible catenary degrees of the elements of an affine semigroup of this kind occur as the catenary degree of one of its Betti elements. <\/jats:p>","DOI":"10.1142\/s0218196713500033","type":"journal-article","created":{"date-parts":[[2012,12,26]],"date-time":"2012-12-26T01:21:35Z","timestamp":1356484895000},"page":"111-122","source":"Crossref","is-referenced-by-count":21,"title":["FACTORIZATION INVARIANTS IN HALF-FACTORIAL AFFINE SEMIGROUPS"],"prefix":"10.1142","volume":"23","author":[{"given":"P. A.","family":"GARC\u00cdA S\u00c1NCHEZ","sequence":"first","affiliation":[{"name":"Departamento de \u00c1lgebra, Universidad de Granada, E-18071 Granada, Spain"}]},{"given":"I.","family":"OJEDA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Extremadura, E-06071 Badajoz, Spain"}]},{"given":"A.","family":"S\u00c1NCHEZ-R.-NAVARRO","sequence":"additional","affiliation":[{"name":"Departamento Lenguajes y Sistemas Inform\u00e1ticos, Universidad de C\u00e1diz, E-11405 Jerez de la Frontera (C\u00e1diz), Spain"}]}],"member":"219","published-online":{"date-parts":[[2013,3,3]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-2010-068-3"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-006-0008-8"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/502\/09855"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2010.248.91"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1201\/9781420003208"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2007.10.020"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2010.02.023"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01273309"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2009.08.009"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-010-9218-1"},{"key":"rf14","volume-title":"Finitely Generated Commutative Monoids","author":"Rosales J. C.","year":"1999"},{"key":"rf15","series-title":"University Lecture Series","volume-title":"Gr\u00f6bner Bases and Convex Polytopes","volume":"8","author":"Sturmfels B.","year":"1996"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196713500033","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:16:28Z","timestamp":1565122588000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196713500033"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2]]},"references-count":12,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2013,3,3]]},"published-print":{"date-parts":[[2013,2]]}},"alternative-id":["10.1142\/S0218196713500033"],"URL":"https:\/\/doi.org\/10.1142\/s0218196713500033","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2]]}}}