Affiliations: [a]
Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran
| [b]
University of Applied Science and Technology, Tehran, Iran
Correspondence:
[*]
Corresponding author. R.A. Borzooei, Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran. Tel.: +98 2129903131; Fax: +98 2122431652; E-mail: [email protected].
Abstract: In this paper, first we investigate some properties of L-ordered groups such as L-subgroup generated by an arbitrary subset and product of L-ordered groups. Then we introduce the notions of totally L-ordered group and strong totally L-ordered group, where L is a frame and some related results are obtained. We show that the set of all isomorphisms on a totally L-subgroup, forms an L-ordered group. Moreover, if it is a strong totally L-ordered group, then the set of all isomorphisms on it is an L-lattice ordered group.
Keywords: Fuzzy order, L-frame, L-lattice ordered group, totally L-ordered group
