Geodesic
N-Prime Spectrum of Stone Almost Distributive Lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 299-320.

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

Introduced the notions of annulets and 𝒩-filters in stone Almost Distributive Lattices and investigated their properties. Utilized annulets to characterize the 𝒩-filters. Derived that every proper 𝒩-filter is the intersection of all 𝒩-prime filters containing it and also proved that the set ℱ_𝒩(L) of all 𝒩-filters is isomorphic to the class Con_E(L) of all G-extentions of L. Given some topological properties of the space of all 𝒩-prime filters. Derived a necessary and sufficient condition for the space of all 𝒩-prime filters to be a Hausdorff space.
Keywords: Almost Distributive Lattice (ADL), stone ADL, ideal, filter, annulet, isomorphism, compact set, Hausdorff space, N-filters 
@article{DMGAA_2021_41_2_a6,
     author = {Rafi, N. and Bandaru, Ravi Kumar and Srujana, M.},
     title = {N-Prime {Spectrum} of {Stone} {Almost} {Distributive} {Lattices}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {299--320},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a6/}
}
TY  - JOUR
AU  - Rafi, N.
AU  - Bandaru, Ravi Kumar
AU  - Srujana, M.
TI  - N-Prime Spectrum of Stone Almost Distributive Lattices
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2021
SP  - 299
EP  - 320
VL  - 41
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a6/
LA  - en
ID  - DMGAA_2021_41_2_a6
ER  - 
%0 Journal Article
%A Rafi, N.
%A Bandaru, Ravi Kumar
%A Srujana, M.
%T N-Prime Spectrum of Stone Almost Distributive Lattices
%J Discussiones Mathematicae. General Algebra and Applications
%D 2021
%P 299-320
%V 41
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a6/
%G en
%F DMGAA_2021_41_2_a6
Rafi, N.; Bandaru, Ravi Kumar; Srujana, M. N-Prime Spectrum of Stone Almost Distributive Lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 299-320. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a6/

[1] A. El-Mohsen Badawy, Extensions of the Glivenko-type congruences on a stone lattice, Math. Meth. Appl. Sci. 41 (15) (2017) 1–14. https://doi.org/10.1002/mma.4492

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

[3] G. Gratzer, General Lattice Theory, (Academic Press, New York, Sanfransisco, 1978).

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

[5] G.C. Rao and S. Ravi Kumar, Minimal prime ideals in Almost Distributive Lattices, Int. J. Contemp. Sci. 4 (2009) 475–484.

[6] 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

[7] U.M. Swamy, G.C. Rao and G. Nanaji Rao, Pseudo-complementation on Almost Distributive Lattices, South. Asian Bull. Math. 24 (2000) 95–104. https://doi.org/10.1007/s10012-000-0095-5

[8] U.M. Swamy, G.C. Rao and G. Nanaji Rao, Stone Almost Distributive Lattices, South. Asian Bull. Math. 27 (2003) 513–526.