On properties of nil subsets in difference algebras - Roh, E. H.; Jun, Y. B.; Kim, S. Y.; Shim, W. H. (Tamkang Journal of Mathematics, 2001)
In this paper, we introduce the concept of nil subsets by using nilpotent elements, and investigate some related properties. We show that a nil subset on a subalgebra (resp. (closed) ideal) is a subalgebra (resp. (closed) ideal). We also prove that in a nil algebra every ideal is a subalgebra.