On The Algebraic Properties of l-Congruencies in Groups

Lee Xu

University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China

Email: Leexu1244@yahoo.com

Abstract

This paper is dedicated to defining and studying the concept of congruencies in l-groups, where we prove the following main results:

1)       If θ is a congruence relation on l-group G, then  is l-group.

2)       If  is l-group, then for  holds:

 if and only if  are equivalent.

Also, we illustrate many examples to clarify the validity of our work.

Keywords: Group; l-Congruence; order relation; Lattice-ordered group.