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The group of units of the ring Z_n

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)
    Keywords: ring Z_n, group of units, cyclic group, primitive root
    Number of Pages: 53
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Primož ŠparlMentor
    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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