A variant of the primitive element theorem for separable extensions of a commutative ring
In this article we show that any strongly separable extension of a commutative ring R can be embedded into another one having primitive element whenever every boolean localization of R modulo its Jacobson radical is von Neumann regular and locally uniform.
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2009 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154618 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A variant of the primitive element theorem for separable extensions of a commutative ring / D. Bagio, A. Paques // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 20–26. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862749505931182080 |
|---|---|
| author | Bagio, D. Paques, A. |
| author_facet | Bagio, D. Paques, A. |
| citation_txt | A variant of the primitive element theorem for separable extensions of a commutative ring / D. Bagio, A. Paques // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 20–26. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this article we show that any strongly separable extension of a commutative ring R can be embedded into another one having primitive element whenever every boolean localization of R modulo its Jacobson radical is von Neumann regular and locally uniform.
|
| first_indexed | 2025-12-07T21:00:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154618 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T21:00:34Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bagio, D. Paques, A. 2019-06-15T16:54:07Z 2019-06-15T16:54:07Z 2009 A variant of the primitive element theorem for separable extensions of a commutative ring / D. Bagio, A. Paques // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 20–26. — Бібліогр.: 12 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:13B05, 12F10 https://nasplib.isofts.kiev.ua/handle/123456789/154618 In this article we show that any strongly separable extension of a commutative ring R can be embedded into another one having primitive element whenever every boolean localization of R modulo its Jacobson radical is von Neumann regular and locally uniform. This paper was partially supported by CAPES (Brazil) en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics A variant of the primitive element theorem for separable extensions of a commutative ring Article published earlier |
| spellingShingle | A variant of the primitive element theorem for separable extensions of a commutative ring Bagio, D. Paques, A. |
| title | A variant of the primitive element theorem for separable extensions of a commutative ring |
| title_full | A variant of the primitive element theorem for separable extensions of a commutative ring |
| title_fullStr | A variant of the primitive element theorem for separable extensions of a commutative ring |
| title_full_unstemmed | A variant of the primitive element theorem for separable extensions of a commutative ring |
| title_short | A variant of the primitive element theorem for separable extensions of a commutative ring |
| title_sort | variant of the primitive element theorem for separable extensions of a commutative ring |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154618 |
| work_keys_str_mv | AT bagiod avariantoftheprimitiveelementtheoremforseparableextensionsofacommutativering AT paquesa avariantoftheprimitiveelementtheoremforseparableextensionsofacommutativering AT bagiod variantoftheprimitiveelementtheoremforseparableextensionsofacommutativering AT paquesa variantoftheprimitiveelementtheoremforseparableextensionsofacommutativering |