Cyclotomic equations and square properties in rings
If R is a ring, the structure of the projective special linear group PSL2(R) is used to investigate the existence of sum of square properties holding in R. Rings which satisfy Fermat's two-square theorem are called sum of squares rings and have been studied previously. The present study conside...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128600011X |
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| _version_ | 1832552087447142400 |
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| author | Benjamin Fine |
| author_facet | Benjamin Fine |
| author_sort | Benjamin Fine |
| collection | DOAJ |
| description | If R is a ring, the structure of the projective special linear group PSL2(R) is used to investigate the existence of sum of square properties holding in R. Rings which satisfy Fermat's two-square theorem are called sum of squares rings and have been studied previously. The present study considers a related property called square property one. It is shown that this holds in an infinite class of rings which includes the integers, polynomial rings over many fields and Zpn where P is a prime such that −3 is not a square modp. Finally, it is shown that the class of sum of squares rings and the class satisfying square property one are non-coincidental. |
| format | Article |
| id | doaj-art-82998062d9204b57bcba8606bd8bd458 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-82998062d9204b57bcba8606bd8bd4582025-02-03T05:59:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-0191899510.1155/S016117128600011XCyclotomic equations and square properties in ringsBenjamin Fine0Department of Mathematics, University of California Santa Barbara, Santa Barbara 93106, California, USAIf R is a ring, the structure of the projective special linear group PSL2(R) is used to investigate the existence of sum of square properties holding in R. Rings which satisfy Fermat's two-square theorem are called sum of squares rings and have been studied previously. The present study considers a related property called square property one. It is shown that this holds in an infinite class of rings which includes the integers, polynomial rings over many fields and Zpn where P is a prime such that −3 is not a square modp. Finally, it is shown that the class of sum of squares rings and the class satisfying square property one are non-coincidental.http://dx.doi.org/10.1155/S016117128600011XFermat's two square theoremPSL2(R)trace classsum of squares ringmodular groupfree product of groups. |
| spellingShingle | Benjamin Fine Cyclotomic equations and square properties in rings International Journal of Mathematics and Mathematical Sciences Fermat's two square theorem PSL2(R) trace class sum of squares ring modular group free product of groups. |
| title | Cyclotomic equations and square properties in rings |
| title_full | Cyclotomic equations and square properties in rings |
| title_fullStr | Cyclotomic equations and square properties in rings |
| title_full_unstemmed | Cyclotomic equations and square properties in rings |
| title_short | Cyclotomic equations and square properties in rings |
| title_sort | cyclotomic equations and square properties in rings |
| topic | Fermat's two square theorem PSL2(R) trace class sum of squares ring modular group free product of groups. |
| url | http://dx.doi.org/10.1155/S016117128600011X |
| work_keys_str_mv | AT benjaminfine cyclotomicequationsandsquarepropertiesinrings |