Shahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901VOLUNTARY GE-FILTERS AND FURTHER RESULTS OF GE-FILTERS IN GE-ALGEBRAS3147232010.22044/jas.2021.10357.1511ENA. Borumand SaeidDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid
Bahonar University of Kerman, P.O. Box 76169-14111, Kerman, Iran.0000-0001-9495-6027A. RezaeiDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.0000-0002-6003-3993R. BandaruDepartment of Mathematics, GITAM(Deemed to be University), P.O. Box 502329
Telangana State, India.0000-0001-8661-7914Y. B. JunDepartment of Mathematics Education, Gyeongsang National University, P.O. Box
52828, Jinju, Korea.0000-0002-0181-8969Journal Article20201209Further properties on (belligerent) GE-filters are discussed, and the quotient GEalgebra via a GE-filter is established. Conditions for the set →<br />c to be a belligerent GE-filter<br />are provided. The extension property of belligerent GE-filter is composed. The notions of a<br />balanced element, a balanced GE-filter, an antisymmetric GE-algebra and a voluntary GE-filter<br />are introduced, and its properties are examined. The relationship between a GE-subalgebra<br />and a GE-filter is established. Conditions for every element in a GE-algebra to be a balanced<br />element are provided. The conditions necessary for a GE-filter to be a voluntary GE-filter are<br />considered. The GE-filter generated by a given subset is established, and its shape is identifiedhttps://jas.shahroodut.ac.ir/article_2320_d3dbe1e21cedb80b82201fd26488d9bd.pdf