Document Type : Review Paper

Authors

• Sh. Sajana ¹
• D. Bharathi ²

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 Z_n. 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 Z_n. 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 Z_n 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

Main Subjects

• Other