Research Article
Year 2025,
Volume: 74 Issue: 1, 35 - 46
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.
References
- Birkhoff, G., Lattice Theory, Colloq. Publ., Amer. Math. Soc. Providence, 1940. DOI: https://doi.org/10.1090/coll/025
- Boole, G., An Investigation Into the Laws of Thought, London, 1854 (Reprinted by open court publishing company).
- Burris, S., Sankappanavar, H. P., A First Course in Universal Algebra, Spinger-Verlag, New York, 1981.
- Gratzer, G., General Lattice Theory, Pure and Applied Mathematics, Academic Press, New York, 1978.
- Rao, G. C., Assaye B., Ratnamani, M. V., Heyting almost distributive lattices, Int. J. Comp. Cognition, 8 (2010), 89–93.
- 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
- Rao, G. C., Ratnamani, M. V., Shum, K. P., Almost semi-Heyting algebras, Southeast Asian Bull. Math., 42 (2018), 95–110.
- 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.
- Stone, M. H., A Theory of representations of Boolean algebras, Trans. Am. Math. Soc., 40 (1936), 37–111. DOI: https://doi.org/10.2307/1989664
- Stone, M. H., Topological representation of distributive lattices and Brouwerian logics, Cas. Pest. Math. Fys., 67 (1937), 1–25. DOI: http://eudml.org/doc/27235
- Swamy, U. M., Rao, G. C., Almost distributive lattices, Jour. Asust. Math. Soc., 31 (1981), 77–91. DOI: https://doi.org/10.1017/s1446788700018498
Year 2025,
Volume: 74 Issue: 1, 35 - 46
Abstract
References
- Birkhoff, G., Lattice Theory, Colloq. Publ., Amer. Math. Soc. Providence, 1940. DOI: https://doi.org/10.1090/coll/025
- Boole, G., An Investigation Into the Laws of Thought, London, 1854 (Reprinted by open court publishing company).
- Burris, S., Sankappanavar, H. P., A First Course in Universal Algebra, Spinger-Verlag, New York, 1981.
- Gratzer, G., General Lattice Theory, Pure and Applied Mathematics, Academic Press, New York, 1978.
- Rao, G. C., Assaye B., Ratnamani, M. V., Heyting almost distributive lattices, Int. J. Comp. Cognition, 8 (2010), 89–93.
- 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
- Rao, G. C., Ratnamani, M. V., Shum, K. P., Almost semi-Heyting algebras, Southeast Asian Bull. Math., 42 (2018), 95–110.
- 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.
- Stone, M. H., A Theory of representations of Boolean algebras, Trans. Am. Math. Soc., 40 (1936), 37–111. DOI: https://doi.org/10.2307/1989664
- Stone, M. H., Topological representation of distributive lattices and Brouwerian logics, Cas. Pest. Math. Fys., 67 (1937), 1–25. DOI: http://eudml.org/doc/27235
- Swamy, U. M., Rao, G. C., Almost distributive lattices, Jour. Asust. Math. Soc., 31 (1981), 77–91. DOI: https://doi.org/10.1017/s1446788700018498
There are 11 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory, Mathematical Logic, Set Theory, Lattices and Universal Algebra |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | |
| Submission Date | July 1, 2024 |
| Acceptance Date | August 30, 2024 |
| Published in Issue | Year 2025 Volume: 74 Issue: 1 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
