Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 8-16
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0220
Some new results on w Up-algebras
Daniel A. Romano\(^{1,*}\)
\(^{1}\) International Mathematical Virtual Institute \newline Korduna\v ska Street 6, 78000 Banja Luka, Bosnia and Herzegovina; danielromano1949@gmail.com.
Copyright © 2024 Daniel A. Romano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: August 25, 2023 – Accepted: April 6, 2024 – Published: May 15, 2024
Abstract
The concept of weak UP-algebras (shortly wUP-algebra) is an extension of the notion of UP-algebras introduced in 2021 by Iampan and Romano. In this report, an effective extension of a (weak) UP-algebra to a wUP-algebra is created. In addition to the previous one, the concept of atoms in wUP-algebras is introduced and their important properties are registered. Finally, the concept of wUP-filters in wUP-algebras was introduced and its connections with other substructures in wUP-algebras were analyzed.
Keywords:
UP-algebra, weak UP-algebra (shortly wUP-algebra), extension of a (weak) UP-algebra to a wUP-algebra, atoms in wUP-algebras, wUP-filters