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Some Topological Properties of the Spectrum of Prime D-Filters of Distributive Lattices

A. P. Phaneendra Kumar *, M. Sambasiva Rao **, K. Sobhan Babu ***

* Department of Mathematics, Vignan's Institute of Engineering for Women, Vishakapatnam, Andhra Pradesh, India.

** Department of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh, India.

*** Department of Mathematics, JNTU-K University College of Engineering, Guntur, Andhra Pradesh, India.

Periodicity:January - June'2021
DOI : https://doi.org/10.26634/jmat.10.1.18165

Abstract

Some properties of prime D-filters of distributive lattices are studied with respect to the direct products and set-theoretic intersection. Properties of minimal prime D-filters of distributive lattices are studied. Some topological properties of the space of all minimal prime D-filters of a distributive lattice are studied. Finally, it is showed that the space of all minimal prime D-filters of a distributive lattice is a Hausdorff space.

Keywords

Dense Element, Flter, D-filter, Prime D-filter, Direct Product, Hausdorff Space.

How to Cite this Article?

Kumar, A. P. P., Rao, M. S., and Babu, K. S. (2021). Some Topological Properties of the Spectrum of Prime D-Filters of Distributive Lattices. i-manager's Journal on Mathematics, 10(1), 22-31. https://doi.org/10.26634/jmat.10.1.18165

References

[1]. Birkhoff, G. (1967). Lattice Theory. American Mathematical Society Colloquium Publications.

[2]. Cornish, W. H. (1972). Normal lattices. Journal of the Australian Mathematical Society, 14(2), 200-215.

[3]. Cornish, W. H. (1974). Quasi complemented lattices. Commentationes Mathematicae Universitatis Carolinae, 15(3), 501-511.

[4]. Cornish, W. H. (2009). Annulets and α-ideals in distributive lattices. Journal of the Australian Mathematical Society, 15, 70-77.

[5]. Katrinak, T. (1966). Remarks on stone lattices I. Mathematical and Physical Proceedings (in Russian), 16(2), 128-142.

[6]. Kist, J. (1963). Minimal prime ideals in commutative semigroups. Proceedings of the London Mathematical Society, s3-13(1), 31-50.

[7]. Kumar, A. P. P., Rao, M. S., & Babu, K. S. (in press). Filters of distributive lattices generated by dense elements. Palestine Journal of Mathematics.

[8]. Kumar, A. P. P., Rao, M. S., & Babu, K. S. (2021). Generalized prime D-filters of diistributive lattice. Archivum Mathematicum. 57(3), 157–174.

[9]. Mandelker, M. (1970). Relative annihilators in lattices. Duke Mathematical Journal, 37(2), 377-386.

[10]. Rao, M. S. (2012). Normal filters of distributive lattice. Bulletin of the Section of Logic. 41(3-4), 131-143.

[11]. Rao, M. S. (2013). e-filters of MS-algebras. Acta Mathematica Scientia, 33(3), 738-746.

[12]. Rao, M. S., & Badawy, A. E. M. (2016). μ-Filters of distributive lattices. Southeast Asian Bulletin of Mathematics, 40(2), 251-264.

[13]. Rao, M. S., & Shum, K. P. (2013). Boolean filters of distributive lattices. International Journal of Mathematics and Soft Computing, 3, 41-48.

[14]. Sankappanavar, H. P., & Burris, S. (1981). A course in universal algebra. Graduate Texts Math.

[15]. Speed, T. P. (1969). Some remarks on a class of distributive lattices. Journal of the Australian Mathematical Society, 9(3-4), 289-296.

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Some Topological Properties of the Spectrum of Prime D-Filters of Distributive Lattices

Abstract

Keywords

How to Cite this Article?

References

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