The space of minimal prime $D$−filters of Almost Distributive Lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 343-368.

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

The concept of D-filters is introduced in an Almost Distributive Lattice (ADL) and studied their properties. An equivalency is established between the minimal prime D-filters of an ADL and its quotient ADL with respect to a congruence. Finally, some properties of prime D-filters and minimal prime D-filters of an ADL are studied topologically.
Keywords: Almost Distributive Lattice (ADL), prime filter, D-filter, D-normal ADL, congruence, compact, Hausdorff space, closure
@article{DMGAA_2024_44_2_a7,
     author = {Rafi, N. and Vijaya Saradhi, P. and Balaiah, M.},
     title = {The space of minimal prime $D$\ensuremath{-}filters of {Almost} {Distributive} {Lattices}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {343--368},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a7/}
}
TY  - JOUR
AU  - Rafi, N.
AU  - Vijaya Saradhi, P.
AU  - Balaiah, M.
TI  - The space of minimal prime $D$−filters of Almost Distributive Lattices
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2024
SP  - 343
EP  - 368
VL  - 44
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a7/
LA  - en
ID  - DMGAA_2024_44_2_a7
ER  - 
%0 Journal Article
%A Rafi, N.
%A Vijaya Saradhi, P.
%A Balaiah, M.
%T The space of minimal prime $D$−filters of Almost Distributive Lattices
%J Discussiones Mathematicae. General Algebra and Applications
%D 2024
%P 343-368
%V 44
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a7/
%G en
%F DMGAA_2024_44_2_a7
Rafi, N.; Vijaya Saradhi, P.; Balaiah, M. The space of minimal prime $D$−filters of Almost Distributive Lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 343-368. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a7/

[1] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ. XXV (Providence, 1967), USA.

[2] W.H. Cornish, Normal lattices, J. Aust. Math. Soc. 16 (1972) 200–215. https://doi.org/10.1017/S1446788700010041

[3] G. Gratzer, General Lattice Theory (Academic Press, New York, Sanfransisco, 1978). https://doi.org/10.1007/978-3-0348-7633-9

[4] A.P. Phaneendra 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

[5] G.C. Rao, Almost Distributive Lattices, Doctoral Thesis (Dept. of Mathematics, Andhra University, Visakhapatnam, 1980).

[6] G.C. Rao and S. Ravi Kumar, Minimal prime ideals in an ADL, Int. J. Contemp. Sciences 4 (2009) 475–484.

[7] G.C. Rao and S. Ravi Kumar, Normal Almost Distributive Lattices, South. Asian Bull. Math. 32 (2008) 831–841.

[8] G.C. Rao and M. Sambasiva Rao, Annulets in Almost Distributive Lattices, Eur. J. Pure Appl. Math. 2(1) (2009) 58–72.

[9] U.M. Swamy and G.C. Rao, Almost Distributive Lattices, J. Aust. Math. Soc. (Ser. A), 31 (1981) 77–91. https://doi.org/10.1017/S1446788700018498