Abstract
The concept of $MS$-intervals and its properties on $MS$-algebras are introduced and the connection between an $MS$-algebra and the family of its $MS$-intervals is established.
Keywords
distributive lattices boolean algebras de Morgan algebras $MS$-algebras ideals congruence relations interval algebra
References
- [1] A. Badawy, On a construction of modular GMS-algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 54 (1), 19–31, 2015.
- [2] A. Badawy, On a certain Triple construction GMS-algebras, Appl. Math. Inf. Sci. Lett. 3 (3), 115–121, 2015.
- [3] A. Badawy and R. El-Fawal, Homomorphism and Subalgebras of decomposable MSalgebras, J. Egypt. Math. Soc. 25, 119–124, 2017.
- [4] A. Badawy and M.S. Rao, Closure ideals of MS-algebras, Chamchuri J. Math. 6, 31–46, 2014.
- [5] A. Badawy, D. Guffova and M. Haviar, Triple construction of decomposable MSalgebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 51 (2), 53–65, 2012.
- [6] J. Berman, Notes on equational classes of algebras, Lecture Notes, Univ. of Chicago, 1974.
- [7] T.S. Blyth, Lattices and ordered Algebric Structures, Springer-Verlag, London Limited, 2005.
- [8] T.S. Blyth and J.C. Varlet, On a common abstraction of de Morgan algebras and Stone algebras, Proc. Roy. Soc. Edinburgh, 94A, 301–308, 1983.
- [9] T.S. Blyth and J.C. Varlet, Subvarieties of the class of MS-algebras, Proc. Roy. Soc. Edinburgh, 95A, 157–169, 1983.
- [10] T.S. Blyth and J.C. Varlet, Fixed points of MS-algebras, Bull. Soc. Roy. Sci. Liege, 53, 1–8, 1984.
- [11] T.S. Blyth and J.C. Varlet, The ideal lattice of an MS-algebra, Glasgow Math. J. 30, 137–143, 1988.
- [12] T.S. Blyth and J.C. Varlet, Ockham Algebras, Oxford University Press, London, 1994.
- [13] L. Congwen, Stonean kernels of MS-algebras, Wuhan Univ. J. Nat. Sci. 3 (4), 394–396, 1998.
- [14] G. Gr¨atzer, Lattice theory, first concepts and distributive lattices, Lecture Notes, Freeman, San Francisco, California, 1971.
Abstract
References
- [1] A. Badawy, On a construction of modular GMS-algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 54 (1), 19–31, 2015.
- [2] A. Badawy, On a certain Triple construction GMS-algebras, Appl. Math. Inf. Sci. Lett. 3 (3), 115–121, 2015.
- [3] A. Badawy and R. El-Fawal, Homomorphism and Subalgebras of decomposable MSalgebras, J. Egypt. Math. Soc. 25, 119–124, 2017.
- [4] A. Badawy and M.S. Rao, Closure ideals of MS-algebras, Chamchuri J. Math. 6, 31–46, 2014.
- [5] A. Badawy, D. Guffova and M. Haviar, Triple construction of decomposable MSalgebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 51 (2), 53–65, 2012.
- [6] J. Berman, Notes on equational classes of algebras, Lecture Notes, Univ. of Chicago, 1974.
- [7] T.S. Blyth, Lattices and ordered Algebric Structures, Springer-Verlag, London Limited, 2005.
- [8] T.S. Blyth and J.C. Varlet, On a common abstraction of de Morgan algebras and Stone algebras, Proc. Roy. Soc. Edinburgh, 94A, 301–308, 1983.
- [9] T.S. Blyth and J.C. Varlet, Subvarieties of the class of MS-algebras, Proc. Roy. Soc. Edinburgh, 95A, 157–169, 1983.
- [10] T.S. Blyth and J.C. Varlet, Fixed points of MS-algebras, Bull. Soc. Roy. Sci. Liege, 53, 1–8, 1984.
- [11] T.S. Blyth and J.C. Varlet, The ideal lattice of an MS-algebra, Glasgow Math. J. 30, 137–143, 1988.
- [12] T.S. Blyth and J.C. Varlet, Ockham Algebras, Oxford University Press, London, 1994.
- [13] L. Congwen, Stonean kernels of MS-algebras, Wuhan Univ. J. Nat. Sci. 3 (4), 394–396, 1998.
- [14] G. Gr¨atzer, Lattice theory, first concepts and distributive lattices, Lecture Notes, Freeman, San Francisco, California, 1971.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | October 8, 2019 |
| Published in Issue | Year 2019 Volume: 48 Issue: 5 |