%0 Journal Article %T Description of $J$-sets and $C$-sets by matrices %J Khayyam Journal of Mathematics %I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures) %Z 2423-4788 %A Hosseini, Hedieh %A Akbari Tootkaboni, Mohammad %D 2022 %\ 07/01/2022 %V 8 %N 2 %P 174-177 %! Description of $J$-sets and $C$-sets by matrices %K $J$-set %K $C$-set %R 10.22034/kjm.2022.295836.2328 %X  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 $S$. %U https://www.kjm-math.org/article_154684_6a79c01fbe2a885221a21cc11a5897a5.pdf