@article {
author = {Sajana, Sh. and Bharathi, D.},
title = {Number theoretic properties of the commutative ring Zn},
journal = {International Journal of Research in Industrial Engineering},
volume = {8},
number = {1},
pages = {77-88},
year = {2019},
publisher = {Ayandegan Institute of Higher Education, Iran},
issn = {1925-7805},
eissn = {1925-7813},
doi = {10.22105/riej.2019.159539.1065},
abstract = {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.},
keywords = {Non-unit elements,Non-trivial divisor,Least common multiple,Congruent,Finite commutative ring,Principal ideal},
url = {http://www.riejournal.com/article_82715.html},
eprint = {http://www.riejournal.com/article_82715_6f89f08db04192791669b09068bfe607.pdf}
}