Arithmetic in the ring of Gaussian integers
| dc.contributor.author | Molelekeng, Beverly | |
| dc.date.accessioned | 2022-12-21T09:41:12Z | |
| dc.date.available | 2022-12-21T09:41:12Z | |
| dc.date.issued | 2022 | |
| dc.description | A research report submitted to the School of Mathematics, Faculty of Science, University of Witwatersrand, in partial fulfilment of the requirements for the degree Master of Science, 2022 | |
| dc.description.abstract | We study the ring of integers Z, and use it’s properties along with those of complex numbers to explore the nature of the ring of Gaussian integers Z[i]. We introduce an analogue of the key concepts of the ring Z in Z[i] such as factorization and modular arithmetic. One approach is by mimicking the statements and proofs in Z and modifying them to accommodate the 2-dimensional aspect of the elements of Z[i]. Then we investigate ways of extending this information to general quadratic rings of the form Z [√d], whered is a square-free integer. | |
| dc.description.librarian | CK2022 | |
| dc.faculty | Faculty of Science | |
| dc.identifier.uri | https://hdl.handle.net/10539/33915 | |
| dc.language.iso | en | |
| dc.school | School of Mathematics | |
| dc.title | Arithmetic in the ring of Gaussian integers | |
| dc.type | Thesis |