Article,
Epimorphisms in the Category of l-Groups
ALGEBRA COLLOQUIUM, 16 (1): 123-130 (March 2009)
Abstract
In the category of l-groups, we introduce the concepts of Hopfian and generalized Hopfian l-groups. An l-group G is called Hopfian if every surjective l-homomorphism f : G -> G is an l-isomorphism, and G is called generalized Hopfian if every surjective l-homomorphism f : G -> G has a small kernel in G. By an example we show that the class of generalized Hopfian l-groups is a proper subclass of Hopfian l-groups. In this paper, we establish some characterizations for them, which generalize some results in9.
