Generalized Birkhoff Center of Almost Distributive Lattices

Authors

  • Berhanu Assaye Alaba

Abstract

In this paper we define sectional Birkhoff center for an Almost Distributive Lattice not necessarily with maximal elements; as a Birkhoff center of its principal ideals. Moreover we extend this result and define the generalized Birkhoff center of an ADL not necessarily with maximal elements. We give a necessary and sufficient condition for an ADL to be relatively complemented in terms of its sectional Birkhoff centers. Also we define and characterize sectionaly complemented ideals and sectional factor congruences using sectional Birkhoff centers.


MSC-2010: 06D99


Key words: Birkhoff center of ADLs; Sectional Birkhoff center of ADLs; generalized Birkhoff center of ADLs.

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Published

2019-03-22

How to Cite

Alaba, B. A. (2019). Generalized Birkhoff Center of Almost Distributive Lattices. Journal of Global Research in Mathematical Archives(JGRMA), 6(3), 24–33. Retrieved from https://www.jgrma.com/index.php/jgrma/article/view/530

Issue

Vol. 6 No. 3 (2019): March-2019

Section

Research Paper

License

Open Access: This is an open-access journal. All articles published in the Journal of Global Research in Mathematical Archives(JGRMA) are made immediately and permanently available under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. Authors retain the copyright of their work and grant Journal of Global Research in Mathematical Archives(JGRMA)  the right of first publication. This license permits unrestricted use, distribution, adaptation, and reproduction in any medium or format, including commercial use, provided the original author(s), source, and license are properly acknowledged.

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