{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T03:14:24Z","timestamp":1649214864567},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1998,4]]},"abstract":"<jats:p> This paper describes a derivation process for varieties and equational theories using the theory of hypersubstitutions and M-hyperidentities. A hypersubstitution \u03c3 of type \u03c4 is a map which takes each n-ary operation symbol of the type to an n-ary term of this type. If [Formula: see text] is an algebra of type \u03c4 then the algebra [Formula: see text] is called a derived algebra of [Formula: see text]. If V is a class of algebras of type \u03c4 then one can consider the variety v<jats:sub>\u03c3<\/jats:sub>(V) generated by the class of all derived algebras from V. In the first two sections the necessary definitions are given. In Sec. 3 the properties of derived varieties and derived equational theories are described. On the set of all derived varieties of a given variety, a quasiorder is developed which gives a derivation diagram. In the final section the derivation diagram for the largest solid variety of medial semigroups is worked out. <\/jats:p>","DOI":"10.1142\/s0218196798000090","type":"journal-article","created":{"date-parts":[[2003,7,31]],"date-time":"2003-07-31T10:08:41Z","timestamp":1059646121000},"page":"153-169","source":"Crossref","is-referenced-by-count":1,"title":["Derived Varieties and Derived Equational Theories"],"prefix":"10.1142","volume":"08","author":[{"given":"K.","family":"Denecke","sequence":"first","affiliation":[{"name":"University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany"}]},{"given":"J.","family":"Koppitz","sequence":"additional","affiliation":[{"name":"University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany"}]},{"given":"R.","family":"Marsza\u0142ek","sequence":"additional","affiliation":[{"name":"University of Wroc\u0142aw, Institute of Mathematics, pl. Grunwaldzki 2\/4 Wroc\u0142aw, Poland"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573671"},{"key":"p_5","first-page":"7","volume":"2","author":"Graczyriska E.","year":"1990","journal-title":"Algebra Universalis"},{"key":"p_6","first-page":"106","author":"Plonka J.","year":"1994","journal-title":"Palacky University Olomouc"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02188010"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196798000090","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:54:45Z","timestamp":1565128485000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196798000090"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,4]]},"references-count":4,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1998,4]]}},"alternative-id":["10.1142\/S0218196798000090"],"URL":"https:\/\/doi.org\/10.1142\/s0218196798000090","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,4]]}}}