Geodesic
Strongly algebraically closed lattices in $\ell$-groups and semilattices
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 2, pp. 258-263 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this article, the properties of being $\aleph_0$-classes of a full $\ell$-group, the set of polars of an $\ell$-group, the complemented $\ell$-ideals of a complete $\ell$-group, the set of invariant elements of a dimension ortholattice, and pseudocomplemented semilattices are studied from the perspective of model theory and their relations to strongly algebraically closed lattices are obtained.
Keywords: strongly algebraically closed lattices, $\ell$-groups, pseudocomplemented semilattices. 
@article{JSFU_2018_11_2_a15,
     author = {Ali Molkhasi},
     title = {Strongly algebraically closed lattices in $\ell$-groups and semilattices},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {258--263},
     year = {2018},
     volume = {11},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a15/}
}
TY  - JOUR
AU  - Ali Molkhasi
TI  - Strongly algebraically closed lattices in $\ell$-groups and semilattices
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2018
SP  - 258
EP  - 263
VL  - 11
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a15/
LA  - en
ID  - JSFU_2018_11_2_a15
ER  - 
%0 Journal Article
%A Ali Molkhasi
%T Strongly algebraically closed lattices in $\ell$-groups and semilattices
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2018
%P 258-263
%V 11
%N 2
%U http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a15/
%G en
%F JSFU_2018_11_2_a15
Ali Molkhasi. Strongly algebraically closed lattices in $\ell$-groups and semilattices. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 2, pp. 258-263. http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a15/

[1] G.Birkhoff, Lattice theory, American Mathematical Society Colloquium Publications, 25, 3rd ed., American Mathematical Society, New York, 1967 | MR | Zbl

[2] E.Daniyarova, A.Myasnikov, V.Remeslennikov, “Unification theorems in algebraic geometry”, Algebra and Discrete Mathamatics, 2008, 80–112 | MR

[3] E.Daniyarova, A.Myasnikov, V.Remeslennikov, Algebraic geometry over algebraic structures, II: Fundations, arXiv: 1002.3562v2 [math.AG] | MR

[4] E.Daniyarova, A.Myasnikov, V.Remeslennikov, Algebraic geometry over algebraic structures, III: Equationally Noetherian property and compactness, arXiv: 1002.4243v2 [math.AG] | MR

[5] E.Daniyarova, A.Myasnikov, V.Remeslennikov, Algebraic geometry over algebraic structures, IV: Equatinal domains and co-domains, preprint, 2012 | MR

[6] A.Fernandez Lopez, M.I.Tocon Barroso, “Pseudocomplemented semilattices, Boolean algebras, and compatible products 1”, Journal of algebra, 242 (2001), 60–91 | DOI | MR | Zbl

[7] S.Givant, P.Halmos, Introduction to Boolean algebras, Springer Science $+$ Business Media, New York, 2009 | MR | Zbl

[8] G.Higman, E.L.Scott, Existentially closed groups, Clarendon Press, 1988 | MR | Zbl

[9] W.Hodges, Model theory, University Press, Cambridge, 1993 | MR | Zbl

[10] A.Molkhasi, “On strongly algebraically closed lattices”, Journal of Siberian Federal University, Mathematics and Physics, 9:2 (2016), 202–208 | DOI | MR

[11] R.Sikorski, Boolean algebras, Springer-Verlag, Berlin etc., 1964 | MR | Zbl

[12] J.Schmid, “Algebraically and existentially closed distributive lattices”, Zeilschr. Math. Logik und Grundlagen d. Math. Bd., 25 (1979), 525–530 | DOI | MR | Zbl

[13] D.A.Vladimirov, Boolean algebras, Nauka, M., 1969 (in Russian) | MR

[14] L.J.M.Waaijers, On the structure of lattice ordered groups, Waltman, 1968 | MR