Commenced in January 2007
Paper Count: 31103
Assessing the Relation between Theory of Multiple Algebras and Universal Algebras
Authors: Mona Taheri
Abstract:In this study, we examine multiple algebras and algebraic structures derived from them and by stating a theory on multiple algebras; we will show that the theory of multiple algebras is a natural extension of the theory of universal algebras. Also, we will treat equivalence relations on multiple algebras, for which the quotient constructed modulo them is a universal algebra and will study the basic relation and the fundamental algebra in question. In this study, by stating the characteristic theorem of multiple algebras, we show that the theory of multiple algebras is a natural extension of the theory of universal algebras.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060555Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 895
 Hansoul, G.E., "A simultaneous characterization of subalgebras and conditional subalgebra of a multialgebra", Bull. Soc. Roy. Sci. Liege., 50 (1981) 16-19.
 Hansoul, G.E., "A subdirect decomposition theorem for multialgebras", algebra universalis. , 16 (1983) 275-281.
 Hoft. H.; Howard, P.E., "Representing multialgebras by algebras, the axiom of choice and the axiom of dependent choice", algebra universal. , 13 (1981) 69-77.
 Schweigert, D., "Congruence relations of multialgebra", Discrete Math., 53 (1985)249-2523.
 Walicki, M.; Bialasik, M., "Relations, multialgebra and homomorphisms", material bibliografic dicponibil pe internet la adresa http://www.ii.uib.no/ ~michal/.
 Breaz, S.; Pelea, C., "Multialgebras and term function over the algebra of their nonvoid subsets", Mathematica (cluj)., 43 (2001) 143-149.
 Pelea, C., "Construction of multialgebra", PhD Thesis summary (2003).
 Pelea, C., "Identities of multialgebra", Ital. J. Pure Appl. Math., 15 (2004) 83-92.
 Pelea, C., "On the direct product of multialgebra", Studia Univ. Babes- Bolyai Math., 48 (2003) 93-98.
 Pelea, C., "On the functional relation of multialgebra", Ital. J. Pure Appl. Math., 10 (2001) 141-146.
 Gratzer, G., "A representation theorem for multialgebras" , Arch. Math., 3 (1962) 452-456.