{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,17]],"date-time":"2024-03-17T04:10:01Z","timestamp":1710648601662},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:p>The dimension of a variety V of algebras of a given type was introduced by E. Graczy\u0144ska and D. Schweigert in [7] as the cardinality of the set of all derived varieties of V which are properly contained in V. In this paper, we characterize all solid varieties of dimensions 0, 1, and 2; prove that the dimension of a variety of finite type is at most \u2135<jats:sub>0<\/jats:sub>; give an example of a variety which has infinite dimension; and show that for every n \u2208 \u2115 there is a variety with dimension n. Finally, we show that the dimension of a variety is related to the concept of the semantical kernel of a hypersubstitution and apply this connection to calculate the dimension of the class of all algebras of type \u03c4 = (n).<\/jats:p>","DOI":"10.1142\/s0218196709005342","type":"journal-article","created":{"date-parts":[[2009,10,14]],"date-time":"2009-10-14T09:32:19Z","timestamp":1255512739000},"page":"841-854","source":"Crossref","is-referenced-by-count":0,"title":["THE DIMENSION OF A VARIETY AND THE KERNEL OF A HYPERSUBSTITUTION"],"prefix":"10.1142","volume":"19","author":[{"given":"K.","family":"DENECKE","sequence":"first","affiliation":[{"name":"University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany"}]},{"given":"S. L.","family":"WISMATH","sequence":"additional","affiliation":[{"name":"Department of Mathematics and C.S., University of Lethbridge, Lethbridge, AB., T1K-3M4, Canada"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196702001218"},{"key":"rf2","first-page":"301","volume":"2","author":"Denecke K.","journal-title":"Scientiae Mathematicae Japonicae"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.7151\/dmgaa.1036"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.7151\/dmgaa.1114"},{"key":"rf5","doi-asserted-by":"crossref","DOI":"10.1201\/9781482287516","volume-title":"Hyperidentities and Clones","author":"Denecke K.","year":"2000"},{"key":"rf6","first-page":"323","volume":"3","author":"Gerhard J. A.","journal-title":"Prod. London Math. Soc."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.7151\/dmgaa.1117"},{"key":"rf8","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198511946.001.0001","volume-title":"Fundamentals of Semigroup Theory","author":"Howie J. M.","year":"1995"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.2307\/2311743"},{"key":"rf10","volume-title":"M-Solid Varieties","author":"Koppitz J.","year":"2006"},{"key":"rf13","first-page":"105","volume":"17","author":"Wismath S. L.","journal-title":"Discussiones Mathematicae \u2014 Algebra Stoch. Meth."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005342","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,17]],"date-time":"2024-03-17T03:30:56Z","timestamp":1710646256000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005342"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":11,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,9]]}},"alternative-id":["10.1142\/S0218196709005342"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005342","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}