Document Type : Original Article
Department of Mathematics, Faculty of Sciences, Shahed University
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan
We redefine the notion of $J$-sets in a commutative semigroup $S$ with the help of matrices whose entries are functions from the natural numbers into $S$. We show that our definition of $J$-sets is equivalent to the standard definition of $J$-sets. We also introduce a new notion of $C$-set using matrices whose entries are functions from the natural numbers into $S$.