Number theoretic properties of the commutative ring Zn

Document Type: Review Paper

Authors

1 Department of Mathematics and Statistics, P.R. Govt. College (A), Kakinada, Andhra Pradesh, India.

2 Department of Mathematics, S.V. University, Tirupati, Andhra Pradesh, India.

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.

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