$\mathcal{N}$-ideals of almost distributive lattices

Document Type : Research Paper

Authors

1 Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 102.

2 Department of Mathematics, University of Gondar, Gondar, Ethiopia.

3 Department of Mathematics, Mohan Babu University, A. Rangampet, Tirupati, Andhra Pradesh, India-517 102.

Abstract

In this article, we present the concept of an $\mathcal{N}$-ideal within the structure of an Almost Distributive Lattice (ADL). We demonstrate that the collection of $\mathcal{N}$-ideals constitutes a distributive lattice, which is distinct from and not a sublattice of the lattice of ideals in an ADL. Additionally, we define $\mathcal{N}$-lets in ADLs. We derive the necessary and sufficient conditions for an ideal to be classified as an $\mathcal{N}$-ideal using $\mathcal{N}$-lets. Finally, we establish the conditions required for an ADL to achieve the property of being soft relatively complemented.

Keywords

References

[1] G. Birkhoff, Lattice Theory, 3rd ed., American Mathematical Society, colloquium publications, New York, 1967.
[2] G. Gratzer, General Lattice Theory, Academic Press, inc. New York, 1978.
[3] Y. S. Pawar, The space of maximal ideals in an almost distributive lattice, Int. Math. Forum., 6 No. 28 (2011) 1387-1396.
[4] Y. S. Pawar and I. A. Shaikh, On prime, minimal prime and annihilator ideal in an almost distributive lattices, Eur. J. Pure Appl. Math., 6 No. 1 (2013) 107-118.
[5] N. Rafi and R. K. Bandaru, μ-filters of almost distributive lattices, Chamchuri J. Math., 10 (2018) 53-65.
[6] N. Rafi, Y. Monikarchana and R. K. Bandaru, ν-ideals of Almost Distributive Lattices, Accepted for Publication in Palestine Journal of Mathematics.
[7] G. C. Rao, Almost Distributive Lattices, Doctoral Thesis, Department of Mathematics, Andhra University, Visakhapatnam, 1980.
[8] G. C. Rao and S. R. Kumar, Minimal prime ideals in almost distributive lattices, Int. J. Contemp. Sci., 4 No. 10 (2009) 475-484.
[9] G. C. Rao and M. S. Rao, Annulets in almost distributive lattices, Eur. J. Pure Appl. Math., 2 No. 1 (2009) 58-72.
[10] U. M. Swamy and G. C. Rao, Almost distributive lattices, Jour. Aust. Math. Soc., 31 No. 1 (1981) 77-91.
Algebraic Structures and Their Applications
Volume 12, Issue 2
May 2025
Pages 141-153

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