Geodesic
Interior GE-Filters of GE-Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 217-235.

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

The notions of an interior GE-filter, a weak interior GE-filter and a belligerent interior GE-filter are introduced, and their relations and properties are investigated. Example of a GE-filter which is neither an interior GE-filter nor a weak interior GE-filter is provided. Relations between a weak interior GE-filter and an interior GE-filter are discussed, and conditions under which every weak interior GE-filter is an interior GE-filter are investigated. Relations between a belligerent interior GE-filter and an interior GE-filter are displayed, and conditions for an interior GE-filter to be a belligerent interior GE-filter are considered. Given a subset and an element, an interior GE-filter is established, and conditions for a subset to be a belligerent interior GE-filter are discussed. The extensibility of the beligerant interior GE-filter is debated. Relationships between weak interior GE-filter and belligerent interior GE-filter of type 1, type 2 and type 3 are founded.
Keywords: (transitive, left exchangeable) GE-algebra, GE-filter, belligerent GE-filter, (weak) interior GE-filter, belligerent interior GE-filter (of type 1, type 2 and type 3) 
@article{DMGAA_2022_42_1_a9,
     author = {Song, Seok-Zun and Bandaru, Ravikumar and Romano, Daniel A. and Jun, Young Bae},
     title = {Interior {GE-Filters} of {GE-Algebras}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {217--235},
     publisher = {mathdoc},
     volume = {42},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2022_42_1_a9/}
}
TY  - JOUR
AU  - Song, Seok-Zun
AU  - Bandaru, Ravikumar
AU  - Romano, Daniel A.
AU  - Jun, Young Bae
TI  - Interior GE-Filters of GE-Algebras
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2022
SP  - 217
EP  - 235
VL  - 42
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2022_42_1_a9/
LA  - en
ID  - DMGAA_2022_42_1_a9
ER  - 
%0 Journal Article
%A Song, Seok-Zun
%A Bandaru, Ravikumar
%A Romano, Daniel A.
%A Jun, Young Bae
%T Interior GE-Filters of GE-Algebras
%J Discussiones Mathematicae. General Algebra and Applications
%D 2022
%P 217-235
%V 42
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2022_42_1_a9/
%G en
%F DMGAA_2022_42_1_a9
Song, Seok-Zun; Bandaru, Ravikumar; Romano, Daniel A.; Jun, Young Bae. Interior GE-Filters of GE-Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 217-235. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_1_a9/

[1] R.K. Bandaru, A. Borumand Saeid and Y.B. Jun, On GE-algebras, Bulletin of the Section of Logic 50 (2021) 81–90. https://doi.org/10.18778/0138-0680.2020.20

[2] R.K. Bandaru, A. Borumand Saeid and Y.B. Jun, Belligerent GE-filters in GE-algebras, T. Indones. Math. Soc. (submitted).

[3] G. Castellini and J. Ramos, Interior operators and topological connectedness, Quaest. Math. 33 (2010) 290–304. https://doi.org/10.2989/16073606.2010.507322

[4] A. Diego, Sur algébres de Hilbert, Collect. Logique Math. Ser. A 21 (1967) 177–198.

[5] J.G. Lee, R.K. Bandaru, K. Hur and Y.B. Jun, Interior GE-algebras, J. Math. 2021 (2021) 1–10. https://doi.org/10.1155/2021/6646091

[6] J. Rachůnek and Z. Svoboda, Interior and closure operators on bounded residuated lattices, Cent. Eur. J. Math. 12 (3) (2014) 534–544. https://doi.org/10.2478/s11533-013-0349-y

[7] F. Svrcek, Operators on GMV-algebras, Math. Bohem. 129 (2004) 337–347. https://doi.org/10.21136/MB.2004.134044

[8] S.J.R. Vorster, Interior operators in general categories, Quaest. Math. 23 (2000) 405–416. https://doi.org/10.2989/16073600009485987