Coherent lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 287-299.

Voir la notice de l'article provenant de la source Library of Science

The notion of coherent lattices is introduced and established relations between a coherent lattice and that of a generalized Stone lattice, Boolean algebra, quasi-complemented lattice, and normal lattice. A set of equivalent conditions is given for every sublattice of a lattice to become a coherent lattice. Some equivalent conditions are given for every interval of a lattice to become a coherent sublattice. Coherent lattices are characterized with the help of certain properties of filters and dense elements.
Keywords: Coherent lattice, generalized Stone lattice, Boolean algebra, quasi-complemented lattice, normal lattice
@article{DMGAA_2024_44_2_a3,
     author = {Sambasiva Rao, M. and Siva Rama Raju, S. V.},
     title = {Coherent lattices},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {287--299},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a3/}
}
TY  - JOUR
AU  - Sambasiva Rao, M.
AU  - Siva Rama Raju, S. V.
TI  - Coherent lattices
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2024
SP  - 287
EP  - 299
VL  - 44
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a3/
LA  - en
ID  - DMGAA_2024_44_2_a3
ER  - 
%0 Journal Article
%A Sambasiva Rao, M.
%A Siva Rama Raju, S. V.
%T Coherent lattices
%J Discussiones Mathematicae. General Algebra and Applications
%D 2024
%P 287-299
%V 44
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a3/
%G en
%F DMGAA_2024_44_2_a3
Sambasiva Rao, M.; Siva Rama Raju, S. V. Coherent lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 287-299. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a3/

[1] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. XXV (Providence, USA, 1976).

[2] S. Burris and H.P. Sankappanavar, A Course in Univerasal Algebra (Springer Verlag, 1981).

[3] I. Chajda, R. Halaš and J. Kühr, Semilattice structures (Heldermann Verlag, Germany, 2007). ISBN 978-3-88538-230-0

[4] W.H. Cornish, Normal lattices, J. Austral. Math. Soc. 14 (1973) 167–179. https://doi.org/10.1017/S1446788700010041

[5] W.H. Cornish, Congruences on distributive pseudo-complemented lattices, Bull. Austral. Math. Soc. 8 (1973) 161–179. https://doi.org/10.1017/S0004972700042404

[6] W.H. Cornish, Annulets and \alpha-ideals in distributive lattices, J. Austral. Math. Soc. 15 (1973) 70–77. https://doi.org/10.1017/S1446788700012775

[7] W.H. Cornish, Quasi-complemented lattices, Comm. Math. Univ. Carolinae 15(3) (1974) 501–511. http://dml.cz/dmlcz/105573

[8] O. Frink, Pseudo-complements in semi-lattices, Duke Math. J. 29 (1962) 505–514. https://doi.org/10.1215/S0012-7094-62-02951-4

[9] G. Gratzer, General lattice theory (Academic Press, New York, San Francisco, USA, 1978).

[10] J. Kist, Minimal prime ideals in commutative semigroups, Proc. London Math. Soc., Sec. B 13 (1963) 31–50. https://doi.org/10.1112/plms/s3-13.1.31

[11] M. Mandelker, Relative annihilators in lattices, Duke Math. J. 37 (1970) 377-386. https://doi.org/10.1215/S0012-7094-70-03748-8

[12] A.P. Paneendra Kumar, M. Sambasiva Rao and K. Sobhan Babu, Filters of distributive lattices generated by dense elements, Palestine J. Math. 11(2) (2022) 45–54.

[13] A.P. Paneendra Kumar, M. Sambasiva Rao and K. Sobhan Babu, Generalized prime D-filters of distributive lattices, Archivum Mathematicum 57(3) (2021) 157–174. https://doi.org/10.5817/AM2021-3-157

[14] M. Sambasiva Rao, A note on \sigma -ideals of distributive lattices, Alg. Struct. and their Appl. 9(2) (2022) 163–179. https://doi.org/10.22034/AS.2022.2720

[15] T.P. Speed, Some remarks on a class of distributive lattices, Jour. Aust. Math. Soc. 9 (1969) 289–296. https://doi.org/10.1017/S1446788700007205

[16] M.H. Stone, A theory of representations for Boolean algebras, Tran. Amer. Math. Soc. 40 (1936) 37–111. https://doi.org/10.2307/1989664