journal-of-interdisciplinary-mathematics Journal of Interdisciplinary Mathematics 2169-012X 0972-0502 Taru Publications 10.47974/JIM-1758 Kernel ideals and co-Kernel dual ideals in the variety of MS-almost distributive lattices Addis Gezahagne Mulat Department of Mathematics, University of Gondar, Gondar, P. O. Box: 196, Ethiopia Alemayehu Teferi Getachew Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia Norahun Wondwosen Zemene Department of Mathematics, University of Gondar, Gondar, Ethiopia Boku Dereje Kifle Department of Mathematics, Dilla University, Dilla, Ethiopia Beyene Terefe Getachew Department of Mathematics, Mizan Tepi University, Mizan Tepi, Ethiopia 28 2 457 471 15 03 2025

In this paper, we introduce and provide a comprehensive characterization of Kernel ideals and coKernel dual ideals within the structure of MS-almost distributive lattices. These concepts are examined through the lens of lattice theory, and their properties are explored in relation to congruences and other fundamental operations within the class of ADLs. By defining specific conditions and relations, we establish key properties that distinguish Kernel ideals and coKernel dual ideals, leading to a deeper understanding of their behavior and applications in the context of MS-almost distributive lattices.

 MS-ADLs Kernel ideals Cokernel dual ideals access open retracted no