%0 Journal Article %T Number theoretic properties of the commutative ring Zn %J International Journal of Research in Industrial Engineering %I Ayandegan Institute of Higher Education %Z 2783-1337 %A Sajana, Sh. %A Bharathi, D. %D 2019 %\ 04/01/2019 %V 8 %N 1 %P 77-88 %! Number theoretic properties of the commutative ring Zn %K Non-unit elements %K Non-trivial divisor %K Least common multiple %K Congruent %K Finite commutative ring %K Principal ideal %R 10.22105/riej.2019.159539.1065 %X This paper deals with the number theoretic properties of non-unit elements of the ring Zn. Let D be the set of all non-trivial divisors of a positive integer n. Let D1 and D2 be the subsets of D having the least common multiple which are incongruent to zero modulo n with every other element of D and congruent to zero modulo n with at least one another element of D, respectively. Then D can be written as the disjoint union of D1 and D2 in Zn. We explore the results on these sets based on all the characterizations of n. We obtain a formula for enumerating the cardinality of the set of all non-unit elements in Zn whose principal ideals are equal. Further, we present an algorithm for enumerating these sets of all non-unit elements. %U https://www.riejournal.com/article_82715_6f89f08db04192791669b09068bfe607.pdf