R-ideals of Almost Distributive Lattices

Document Type : Original Manuscript

Authors

1 Department of Mathematics, Siddhartha Academy of Higher Education, Deemed to be University, Vijayawada, Andhra Pradesh, India-520 007.

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

3 Department of Science and Humanities, Vasireddy Venkatadri International Technological University, Guntur, Andhra Pradesh, India-522 508. Email: balaiah_m19@hotmail.com

4 Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 101.

10.22044/jas.2025.14770.1865

Abstract

The concepts have been introduced in Almost Distributive
Lattices(ADLs), namely, R-ideals and -ideals. A set of
conditions has been identified that are equivalent to converting an
E-ideal into an R-ideal. Moreover, it has been derived that for
any E-ideal, there exists a homomorphism with a dual dense kernel,
which is itself an R-ideal. The characterization of -ideals in
terms of R-ideals and congruences has been established. Additionally,
equivalent conditions have been established to demonstrate
that the space of all prime -ideals forms a Hausdorff space.

Keywords

References

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Journal of Algebraic Systems
Volume 14, Issue 3
June 2026
Pages 549-567

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