Geodesic
On a generalized entropic property
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2010), pp. 55-57.

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Let $\cdot, *$ be idempotent operations on the set $A$, and $*$ be a commutative operation. We prove, that if the pair $(\cdot, *)$ satisfies the generalized entropic property, then $(\cdot, *)$ is entropic.
Keywords: complex algebra, entropic algebra, generalized entropic property.
Mots-clés : mode 
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Amir Ehsani. On a generalized entropic property. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2010), pp. 55-57. http://geodesic.mathdoc.fr/item/UZERU_2010_2_a8/

[1] G. Grätzer, H. Lakser, “Identities for globals (complex algebras) of algebras”, Colloq. Math., 56 (1988), 19–29 | MR | Zbl

[2] C. Brink, “Power structures”, Algebra Universalis, 30 (1993), 177–216 | DOI | MR | Zbl

[3] I. Bošnjak, R. Madarász, “On power structures”, Algebra and Discr. Math., 2 (2003), 14–35 | MR

[4] A. Romanowska, J.D.H. Smith, Modal Theory an Algebraic Approach to Order, Geometry and Convexity, Heldermann Verlag, Berlin, 1985 | MR | Zbl

[5] A. Romanowska, J.D.H. Smith, “On the structure of subalgebra systems of idempotent entropic algebras”, J. Algebra, 120 (1989), 263–283 | DOI | MR

[6] A. Romanowska, J.D.H. Smith, On Complex Algebras of Subalgebras, World Scientific, 2002, arXiv: 0610832v1 [math.RA] | MR | MR | Zbl

[7] Yu.M. Movsisyan, Introduction to the Theory of Algebras with Hyperidentities, YSU Press, Yer., 1986 (in Russian) | MR

[8] Yu.M. Movsisyan, Hyperidentities and Hypervarieties in Algebras, YSU Press, Yer., 1990 (in Russian) | MR

[9] Russian Math. Surveys, 53:1 (1998), 57–108 | DOI | DOI | MR | Zbl

[10] J. Ježek, T. Kepka, Medial Groupoids, Rozpravy ČSAV, Praha, 1983, 93 pp. | MR | Zbl

[11] T. J. Evans, “Properties of Algebras Almost Equivalent to Identities”, London Math. Soc., 35 (1962), 53–59 | DOI | MR