TY - JOUR
ID - 82715
TI - Number theoretic properties of the commutative ring Zn
JO - International Journal of Research in Industrial Engineering
JA - RIEJ
LA - en
SN - 2783-1337
AU - Sajana, Sh.
AU - Bharathi, D.
AD - Department of Mathematics and Statistics, P.R. Govt. College (A), Kakinada, Andhra Pradesh, India.
AD - Department of Mathematics, S.V. University, Tirupati, Andhra Pradesh, India.
Y1 - 2019
PY - 2019
VL - 8
IS - 1
SP - 77
EP - 88
KW - Non-unit elements
KW - Non-trivial divisor
KW - Least common multiple
KW - Congruent
KW - Finite commutative ring
KW - Principal ideal
DO - 10.22105/riej.2019.159539.1065
N2 - 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.
UR - https://www.riejournal.com/article_82715.html
L1 - https://www.riejournal.com/article_82715_6f89f08db04192791669b09068bfe607.pdf
ER -