Research Article

Brouwerian almost distributive lattices

Volume: 74 Number: 1 March 8, 2025
EN

Brouwerian almost distributive lattices

Abstract

This paper presents the idea of a Brouwerian almost distributive lattice, a generalization of an almost distributive lattice, and a Brouwerian algebra. We also derive some properties on Brouwerian almost distributive lattices. A set of equivalent conditions is provided for a Brouwerian almost distributive lattice to transform into a Brouwerian algebra.

Keywords

References

  1. Birkhoff, G., Lattice Theory, Colloq. Publ., Amer. Math. Soc. Providence, 1940. DOI: https://doi.org/10.1090/coll/025
  2. Boole, G., An Investigation Into the Laws of Thought, London, 1854 (Reprinted by open court publishing company).
  3. Burris, S., Sankappanavar, H. P., A First Course in Universal Algebra, Spinger-Verlag, New York, 1981.
  4. Gratzer, G., General Lattice Theory, Pure and Applied Mathematics, Academic Press, New York, 1978.
  5. Rao, G. C., Assaye B., Ratnamani, M. V., Heyting almost distributive lattices, Int. J. Comp. Cognition, 8 (2010), 89–93.
  6. Rao, G. C., Ratnamani, M. V., Shum K. P., Assaye, B., Semi-Heyting almost distributive lattices, Lobachevskii J. Math., 36 (2015), 184–189. DOI: https://doi.org/10.1134/S1995080215020158
  7. Rao, G. C., Ratnamani, M. V., Shum, K. P., Almost semi-Heyting algebras, Southeast Asian Bull. Math., 42 (2018), 95–110.
  8. Srikanth, V.V.V.S.S.P.S., Ramesh S., Ratnamani, M. V., Shum, K.P., Semi-Brouwerian almost distributive lattices, Southeast Asian Bull. Math., 48 (2024), 569–578.

Details

Primary Language

English

Subjects

Algebra and Number Theory, Mathematical Logic, Set Theory, Lattices and Universal Algebra

Journal Section

Research Article

Publication Date

March 8, 2025

Submission Date

July 1, 2024

Acceptance Date

August 30, 2024

Published in Issue

Year 2025 Volume: 74 Number: 1

APA
Sirisetti, R., Ramana, L. V., V Ratnamani, M., Bandaru, R., & Alali, A. S. (2025). Brouwerian almost distributive lattices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 74(1), 35-46. https://doi.org/10.31801/cfsuasmas.1506415
AMA
1.Sirisetti R, Ramana LV, V Ratnamani M, Bandaru R, Alali AS. Brouwerian almost distributive lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74(1):35-46. doi:10.31801/cfsuasmas.1506415
Chicago
Sirisetti, Ramesh, L. Venkata Ramana, Mandalika V Ratnamani, Ravikumar Bandaru, and Amal S. Alali. 2025. “Brouwerian Almost Distributive Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 (1): 35-46. https://doi.org/10.31801/cfsuasmas.1506415.
EndNote
Sirisetti R, Ramana LV, V Ratnamani M, Bandaru R, Alali AS (March 1, 2025) Brouwerian almost distributive lattices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 1 35–46.
IEEE
[1]R. Sirisetti, L. V. Ramana, M. V Ratnamani, R. Bandaru, and A. S. Alali, “Brouwerian almost distributive lattices”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 74, no. 1, pp. 35–46, Mar. 2025, doi: 10.31801/cfsuasmas.1506415.
ISNAD
Sirisetti, Ramesh - Ramana, L. Venkata - V Ratnamani, Mandalika - Bandaru, Ravikumar - Alali, Amal S. “Brouwerian Almost Distributive Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74/1 (March 1, 2025): 35-46. https://doi.org/10.31801/cfsuasmas.1506415.
JAMA
1.Sirisetti R, Ramana LV, V Ratnamani M, Bandaru R, Alali AS. Brouwerian almost distributive lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74:35–46.
MLA
Sirisetti, Ramesh, et al. “Brouwerian Almost Distributive Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 1, Mar. 2025, pp. 35-46, doi:10.31801/cfsuasmas.1506415.
Vancouver
1.Ramesh Sirisetti, L. Venkata Ramana, Mandalika V Ratnamani, Ravikumar Bandaru, Amal S. Alali. Brouwerian almost distributive lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025 Mar. 1;74(1):35-46. doi:10.31801/cfsuasmas.1506415