Abstract
The paper characterizes the class of subdirectly irreducible algebras satisfying hyperidentities of the variety of De Morgan algebras. Such algebras are called subdirectly irreducible De Morgan quasilattices. The suggested characterization is quite close to that of the classical case of subdirectly irreducible DeMorgan algebras.
Similar content being viewed by others
References
Yu. M. Movsisyan, Introduction to the Theory of Algebras with Hyperidentities (Russian) (Yerevan State University Press, Yerevan, 1986).
Yu. M. Movsisyan, Hyperidentities and Hypervarieties in Algebras (Russian) (Yerevan State University Press, Yerevan, 1990).
Yu. M. Movsisyan, “Algebras with hyperidentities of the variety of Boolean algebras”, Russ.Acad. Sci Izv. Math., 60, 1219–1260, 1996.
Yu. M. Movsisyan, “Hyperidentities in algebras and varieties, Uspekhi Mat. Nauk, 53(1), 61–114, 1998. English transl. in Russ. Math. Surveys, 53, 57–108, 1998.
G. Birkhoff, Lattice Theory (American Mathematical Society, Providence, 1979).
A. Bialynicki-Birula, H. Rasiowa, “On the representation of quasi-Boolean algebras”, Bull. Acad. Polon. Sci., Ser. Math. Astronom. Phys., 5, 259–261, 1957.
G. C. Moisil, “Recherches sur l’algebre de la logique”, Annales scientifiques de l’universite de Jassy, 22, 1–117, 1935.
H. P. Sankappanavar, “A characterization of principal congruences of DeMorgan algebras and its applications”, Math. Logic in Latin America, Proc. IV Latin Amer. Symp. Math. Logic, Santiago, 341–349, 1978. Nort-Holland, Amsterdam, 1980.
J. A. Brzozowski, “A characterization of De Morgan algebras”, International Journal of Algebra and Computation, 11, 525–527, 2001.
Yu. M. Movsisyan, “Binary representations of algebras with at most two binary operations. A Cayley theorem for distributive lattices”, International Journal of Algebra and Computation, 19, 97–106, 2009.
Yu. M. Movsisyan, V. A. Aslanyan, “Hyperidentities of DeMorgan algebras”, Logic Journal of the IGPL, 20, 1153–1174 (doi:10.1093/jigpal/jzr053), 2012.
Yu. M. Movsisyan, V. A. Aslanyan, “Algebras with hyperidentities of the variety of De Morgan algebras”, Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 48(5), 233–240, 2013.
J. A. Kalman, “Lattices with involution”, Trans. Amer.Math. Soc., 87, 485–491, 1958.
Yu. M. Movsisyan, A. G. Barkhudaryan, “On a hypervariety of QB-algebras”, Uchenye Zapiski YGU, 2, 16–24, 1996.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu. M. Movsisyan, V. A. Aslanyan, 2013, published in Izvestiya NAN Armenii. Matematika, 2013, No. 6, pp. 52–58.
About this article
Cite this article
Movsisyan, Y.M., Aslanyan, V.A. Subdirectly irreducible algebras with hyperidentities of the variety of De Morgan algebras. J. Contemp. Mathemat. Anal. 48, 241–246 (2013). https://doi.org/10.3103/S1068362313060010
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1068362313060010