Radical Classes Closed Under Products
This is a survey of what is known about Kurosh-Amitsur radical classes which are closed under direct products. Associative rings, groups, abelian groups, abelian ℓ-groups and modules are treated. We have attempted to account for all published results relevant to this topic. Many or most of these wer...
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| Format: | Article |
| Language: | English |
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Sciendo
2013-11-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
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| Online Access: | https://doi.org/10.2478/auom-2013-0047 |
| _version_ | 1811272398444429312 |
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| author | Gardner Barry |
| author_facet | Gardner Barry |
| author_sort | Gardner Barry |
| collection | DOAJ |
| description | This is a survey of what is known about Kurosh-Amitsur radical classes which are closed under direct products. Associative rings, groups, abelian groups, abelian ℓ-groups and modules are treated. We have attempted to account for all published results relevant to this topic. Many or most of these were not, as published, expressed in radical theoretic terms, but have consequences for radical theory which we point out. A fruitful source of results and examples is the notion of slenderness for abelian groups together with its several variants for other structures. We also present a few new results, including examples and a demonstration that e-varieties of regular rings are product closed radical classes of associative rings. |
| first_indexed | 2024-04-12T22:39:37Z |
| format | Article |
| id | doaj.art-9865470783504ac9a752bf81b078f39a |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T22:39:37Z |
| publishDate | 2013-11-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-9865470783504ac9a752bf81b078f39a2022-12-22T03:13:46ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352013-11-0121310313210.2478/auom-2013-0047Radical Classes Closed Under ProductsGardner Barry0University of Tasmania Private Bag 37 Hobart, Tas. 7001, AustraliaThis is a survey of what is known about Kurosh-Amitsur radical classes which are closed under direct products. Associative rings, groups, abelian groups, abelian ℓ-groups and modules are treated. We have attempted to account for all published results relevant to this topic. Many or most of these were not, as published, expressed in radical theoretic terms, but have consequences for radical theory which we point out. A fruitful source of results and examples is the notion of slenderness for abelian groups together with its several variants for other structures. We also present a few new results, including examples and a demonstration that e-varieties of regular rings are product closed radical classes of associative rings.https://doi.org/10.2478/auom-2013-0047radical classproductslenderringgroupmodule |
| spellingShingle | Gardner Barry Radical Classes Closed Under Products Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica radical class product slender ring group module |
| title | Radical Classes Closed Under Products |
| title_full | Radical Classes Closed Under Products |
| title_fullStr | Radical Classes Closed Under Products |
| title_full_unstemmed | Radical Classes Closed Under Products |
| title_short | Radical Classes Closed Under Products |
| title_sort | radical classes closed under products |
| topic | radical class product slender ring group module |
| url | https://doi.org/10.2478/auom-2013-0047 |
| work_keys_str_mv | AT gardnerbarry radicalclassesclosedunderproducts |