On strongly algebraically closed lattices
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 2, pp. 202-208
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In this article some fundamental properties of existentially and algebraically closed lattices are investigated. We also define the notion of strongly algebraically closed lattices and we show that a $q'$-compact complete boolean lattice is strongly algebraically closed.
Keywords:
existentially and algebraically closed lattices, strongly algebraically closed lattices, equationally noetherian lattice, complete Boolean algebras.
@article{JSFU_2016_9_2_a8,
author = {Ali Molkhasi},
title = {On strongly algebraically closed lattices},
journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
pages = {202--208},
year = {2016},
volume = {9},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a8/}
}
Ali Molkhasi. On strongly algebraically closed lattices. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 2, pp. 202-208. http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a8/
[1] V. A. Gorbunov, Algebraic theory of quasivarieties, Plenum, New York, 1998 | MR
[2] A. I. Malcev, Algebraic systems, Springer-Verlag, 1973 | MR
[3] A. Miasnikov, V. Rmankov, “Verbally closed subgroups of free groups”, Journal of Group Theory, 17 (2014), 29–40 | MR
[4] J. Schmid, “Algebraically and existentially closed distributive lattices”, Zeilschr. Math. Logik u. G. M., 25 (1979), 525–530 | DOI | MR | Zbl
[5] M. Shahryari, Existentially closed structures and some embedding theorems, 1311.2476
[6] A. Shevlyakov, “Algebraic geometry over boolean algebras in the language with constants”, J. Math. Sciences, 20 (2015), 724–757 | MR