Tilen Miklavec (2019) The group of units of the ring Z_n. MSc thesis.
![]()
| PDF Download (380Kb) |
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) | ||||||
---|---|---|---|---|---|---|---|
Keywords: | ring Z_n, group of units, cyclic group, primitive root | ||||||
Number of Pages: | 53 | ||||||
Language of Content: | Slovenian | ||||||
Mentor / Comentors: |
| ||||||
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 |
Actions (login required)
View Item |