\(a\)-minimal prime ideals in almost distributive lattices
Volume 14, Issue 4, pp 212--221
http://dx.doi.org/10.22436/jnsa.014.04.03
Publication Date: January 05, 2021
Submission Date: November 14, 2020
Revision Date: November 28, 2020
Accteptance Date: December 02, 2020
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Authors
Ch. Santhi Sundar Raj
- Department of Engineering Mathematics, Andhra University, Visakhapatnam, 530003, India.
K. Ramanuja Rao
- Deaprtment of Mathematics, Fiji National Uniersity, Lautoka, FIJI.
S. Nageswara Rao
- Department of Engineering Mathematics, Andhra University, Visakhapatnam, 530003, India.
Abstract
The concept of \(a\)-minimal prime ideal of an ADL is introduced and its characterizations are established. The set of all \(a\)-minimal prime ideals of an ADL is topologized and resulting space is studied.
Share and Cite
ISRP Style
Ch. Santhi Sundar Raj, K. Ramanuja Rao, S. Nageswara Rao, \(a\)-minimal prime ideals in almost distributive lattices, Journal of Nonlinear Sciences and Applications, 14 (2021), no. 4, 212--221
AMA Style
Raj Ch. Santhi Sundar, Rao K. Ramanuja, Rao S. Nageswara, \(a\)-minimal prime ideals in almost distributive lattices. J. Nonlinear Sci. Appl. (2021); 14(4):212--221
Chicago/Turabian Style
Raj, Ch. Santhi Sundar, Rao, K. Ramanuja, Rao, S. Nageswara. "\(a\)-minimal prime ideals in almost distributive lattices." Journal of Nonlinear Sciences and Applications, 14, no. 4 (2021): 212--221
Keywords
- ADL
- minimal prime ideal
- relative
- \(a\)-annihilator
- \(a\)-minimal prime ideal
- \(a\)-maximal filter
- \(a\)-pseudo complementation
- hull-kernel topology
MSC
References
-
[1]
G. Grätzer, General Lattice Theory, Academic Press, New York-London (1978)
-
[2]
M. Mandelker, Relative annhilators in lattices, Duke Math. J., 37 (1970), 377--386
-
[3]
G. C. Rao, S. Ravi Kumar, Minimal prime ideals in Almost Distributive Lattices, Int. J. Contemp. Math. Sci., 4 (2009), 475--484
-
[4]
C. S. Sundar Raj, S. N. Rao, K. R. Rao, $\mathtt{a}$-Maximal filters in Almost Distributive Lattices, J. Int. Math. Virtual Inst., 10 (2020), 309--324
-
[5]
C. S. Sundar Raj, S. N. Rao, K. R. Rao, $\mathtt{a}$-pseudo complementation on an ADL's, Asian-Eur. J. Math., 2020 (2020), (Accepted)
-
[6]
C. S. Sundar Raj, S. N. Rao, M. Santhi, K. R Rao, Relative pseudo-complementations on ADL'S, Int. J. Math. Soft Comput., 7 (2017), 95--108
-
[7]
U. M. Swamy, G. C. Rao, Almost Distributive Lattices, J. Austral. Math. Soc. Ser A, 31 (1981), 77--91
-
[8]
U. M. Swamy, G. C. Rao, G. Nanaji Rao, Pseudo-complementation on Almost Distributive Lattices, Southeast Asian Bull. Math., 24 (2000), 95--104
-
[9]
J. C. Varlet, Relative annihilators in semilattices, Bull. Austral. Math. Soc., 9 (1973), 169--185