{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:38:44Z","timestamp":1753886324957,"version":"3.41.2"},"reference-count":2,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,2,10]],"date-time":"2009-02-10T00:00:00Z","timestamp":1234224000000},"content-version":"vor","delay-in-days":406,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100002842","name":"Chiang Mai University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002842","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>The order of hypersubstitutions, all idempotent elements on the monoid of all hypersubstitutions of type\n<jats:italic>\u03c4<\/jats:italic> = (2) were studied by K. Denecke and Sh. L. Wismath and all idempotent elements on the monoid of all hypersubstitutions of type <jats:italic>\u03c4<\/jats:italic> = (2, 2)\nwere studied by Th. Changpas and K. Denecke. We want to study similar problems for the monoid of all generalized hypersubstitutions\nof type <jats:italic>\u03c4<\/jats:italic> = (2). In this paper, we use similar methods to characterize idempotent generalized\nhypersubstitutions of type <jats:italic>\u03c4<\/jats:italic> = (2) and determine the order of each\ngeneralized hypersubstitution of this type. The main result is\nthat the order is 1,2 or infinite.<\/jats:p>","DOI":"10.1155\/2008\/263541","type":"journal-article","created":{"date-parts":[[2009,2,10]],"date-time":"2009-02-10T17:22:42Z","timestamp":1234286562000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Order of Generalized Hypersubstitutions of Type <i>\u03c4<\/i> = (2)"],"prefix":"10.1155","volume":"2008","author":[{"given":"Wattapong","family":"Puninagool","sequence":"first","affiliation":[]},{"given":"Sorasak","family":"Leeratanavalee","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,2,10]]},"reference":[{"key":"e_1_2_6_1_2","first-page":"135","volume-title":"General Algebra and Applications, Proceedings of the \u201c59th Workshop on \n            General Algebra,\u201d \u201c15th Conference for Young Algebraists Potsdam 2000\u201d","author":"Leeratanavalee S.","year":"2000"},{"key":"e_1_2_6_2_2","first-page":"109","volume-title":"Contributions to General Algebra, 10 (Klagenfurt, 1997)","author":"Denecke K.","year":"1998"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2008\/263541.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2008\/263541.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2008\/263541","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T15:17:23Z","timestamp":1719069443000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2008\/263541"}},"subtitle":[],"editor":[{"given":"Robert","family":"Redfield","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":2,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1155\/2008\/263541"],"URL":"https:\/\/doi.org\/10.1155\/2008\/263541","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2008,1]]},"assertion":[{"value":"2008-08-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-11-11","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-02-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"263541"}}