Tilen Miklavec (2019) *The group of units of the ring Z_n*. MSc thesis.

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## Abstract

In the master’s thesis we study finite rings and their groups of units. The invertible elements of an arbitrary ring with a multiplicative identity form a group for the corresponding multiplicative operation. In the special case of the ring Z_n, this is a group denoted by U_n, also called the group of units. The main purpose of the thesis is to introduce the ring Z_n and to determine, for each integer n, the well known group that the group of units U_n is isomorphic to. We also determine the necessary and suficient condition on n for the group U_n to be cyclic. To this end, we investigate the structure of the group of units U_n and show that we can write it as a direct product of certain cyclic groups. We also indicate how our results can be used for solving some congruence equations.

Item Type: | Thesis (MSc thesis) | ||||||
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Keywords: | ring Z_n, group of units, cyclic group, primitive root | ||||||

Number of Pages: | 53 | ||||||

Language of Content: | Slovenian | ||||||

Mentor / Comentors: |
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Link to COBISS: | https://plus.si.cobiss.net/opac7/bib/peflj/12561225 | ||||||

Institution: | University of Ljubljana | ||||||

Department: | Faculty of Education | ||||||

Item ID: | 5886 | ||||||

Date Deposited: | 23 Aug 2019 14:22 | ||||||

Last Modified: | 23 Aug 2019 14:22 | ||||||

URI: | http://pefprints.pef.uni-lj.si/id/eprint/5886 |

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