{"title":"Assessing the Relation between Theory of Multiple Algebras and Universal Algebras","authors":"Mona Taheri","volume":45,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1317,"pagesEnd":1322,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/5168","abstract":"In this study, we examine multiple algebras and\r\nalgebraic structures derived from them and by stating a theory on\r\nmultiple algebras; we will show that the theory of multiple algebras\r\nis a natural extension of the theory of universal algebras. Also, we\r\nwill treat equivalence relations on multiple algebras, for which the\r\nquotient constructed modulo them is a universal algebra and will\r\nstudy the basic relation and the fundamental algebra in question.\r\nIn this study, by stating the characteristic theorem of multiple\r\nalgebras, we show that the theory of multiple algebras is a natural\r\nextension of the theory of universal algebras.","references":"[1] Hansoul, G.E., \"A simultaneous characterization of subalgebras and\r\nconditional subalgebra of a multialgebra\", Bull. Soc. Roy. Sci. Liege.,\r\n50 (1981) 16-19.\r\n[2] Hansoul, G.E., \"A subdirect decomposition theorem for multialgebras\",\r\nalgebra universalis. , 16 (1983) 275-281.\r\n[3] Hoft. H.; Howard, P.E., \"Representing multialgebras by algebras, the\r\naxiom of choice and the axiom of dependent choice\", algebra universal. ,\r\n13 (1981) 69-77.\r\n[4] Schweigert, D., \"Congruence relations of multialgebra\", Discrete Math.,\r\n53 (1985)249-2523.\r\n[5] Walicki, M.; Bialasik, M., \"Relations, multialgebra and\r\nhomomorphisms\", material bibliografic dicponibil pe internet la adresa\r\nhttp:\/\/www.ii.uib.no\/ ~michal\/.\r\n[6] Breaz, S.; Pelea, C., \"Multialgebras and term function over the algebra\r\nof their nonvoid subsets\", Mathematica (cluj)., 43 (2001) 143-149.\r\n[7] Pelea, C., \"Construction of multialgebra\", PhD Thesis summary (2003).\r\n[8] Pelea, C., \"Identities of multialgebra\", Ital. J. Pure Appl. Math., 15\r\n(2004) 83-92.\r\n[9] Pelea, C., \"On the direct product of multialgebra\", Studia Univ. Babes-\r\nBolyai Math., 48 (2003) 93-98.\r\n[10] Pelea, C., \"On the functional relation of multialgebra\", Ital. J. Pure Appl.\r\nMath., 10 (2001) 141-146.\r\n[11] Gratzer, G., \"A representation theorem for multialgebras\" , Arch. Math.,\r\n3 (1962) 452-456.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 45, 2010"}