APM  Vol.4 No.9 , September 2014
Notes on the Variety of Ternary Algebras
ABSTRACT
In this work we review the class T of ternary algebras introduced by J. A. Brzozowski and C. J. Serger in [1]. We determine properties of the congruence lattice of a ternary algebra A. The most important result refers to the construction of the free ternary algebra on a poset. In particular, we describe the poset of the join irreducible elements of the free ternary algebra with two free generators.

Cite this paper
Figallo, A. , Gomes, C. , Sarmiento, L. and Videla, M. (2014) Notes on the Variety of Ternary Algebras. Advances in Pure Mathematics, 4, 506-512. doi: 10.4236/apm.2014.49057.
References
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http://dx.doi.org/10.1007/978-1-4612-4210-9

[2]   Sankappanavar, H.P. (1980) A Characterization of Principal Congruences of De Morgan Algebras and Its Applications. In: Arruda, A.I., Chuaqui, R. and da Costa, N.C.A., Eds., Mathematical Logic in Latin American, North-Holland Publishing Company, Amsterdam, 341-349.

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[6]   Dilworth, R.P. (1945) Lattices with Unique Complements. Transactions of the American Mathematical Society, 57, 123-154. http://dx.doi.org/10.1090/S0002-9947-1945-0012263-6

[7]   Balbes, R. (2000) Free Ternary Algebras. International Journal of Algebra and Computation, 10, 739-749.
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[8]   Figallo Jr., A. and Ziliani, A. (2011) Free Algebras over a Poset in Varieties. Communications of the Korean Mathematical Society, 26, 543-549.

 
 
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