Description of $J$-sets and $C$-sets by matrices

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Sciences, Shahed University

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan

10.22034/kjm.2022.295836.2328

Abstract

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 $S$.

Keywords