δss-supplemented modules and rings
In this paper, we introduce the concept of δss-supplemented modules and provide the various properties of these modules. In particular, we prove that a ring R is δss-supplemented as a left module if and only if RSoc(RR){R \over {Soc\left( {_RR} \right)}} is semisimple and idempotents lift to Soc(RR)...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2020-12-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2020-0041 |
| _version_ | 1811272243771080704 |
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| author | Türkmen Burcu Nişancı Türkmen Ergül |
| author_facet | Türkmen Burcu Nişancı Türkmen Ergül |
| author_sort | Türkmen Burcu Nişancı |
| collection | DOAJ |
| description | In this paper, we introduce the concept of δss-supplemented modules and provide the various properties of these modules. In particular, we prove that a ring R is δss-supplemented as a left module if and only if RSoc(RR){R \over {Soc\left( {_RR} \right)}} is semisimple and idempotents lift to Soc(RR) if and only if every left R-module is δss-supplemented. We define projective δss-covers and prove the rings with the property that every (simple) module has a projective δss-cover are δss-supplemented. We also study on δss-supplement submodules. |
| first_indexed | 2024-04-12T22:36:49Z |
| format | Article |
| id | doaj.art-10195278b2ff451ab2db1ea8d448faf1 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T22:36:49Z |
| publishDate | 2020-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-10195278b2ff451ab2db1ea8d448faf12022-12-22T03:13:50ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352020-12-0128319321610.2478/auom-2020-0041δss-supplemented modules and ringsTürkmen Burcu Nişancı0Türkmen Ergül1Amasya University, Faculty of Art and Science, Department of Mathematics, Ipekkoy, 05100, Amasya, Turkey.Amasya University, Faculty of Art and Science, Department of Mathematics, Ipekkoy, 05100, Amasya, Turkey.In this paper, we introduce the concept of δss-supplemented modules and provide the various properties of these modules. In particular, we prove that a ring R is δss-supplemented as a left module if and only if RSoc(RR){R \over {Soc\left( {_RR} \right)}} is semisimple and idempotents lift to Soc(RR) if and only if every left R-module is δss-supplemented. We define projective δss-covers and prove the rings with the property that every (simple) module has a projective δss-cover are δss-supplemented. We also study on δss-supplement submodules.https://doi.org/10.2478/auom-2020-0041semisimple modulestrongly δ-local moduleδ ss -supplemented moduleleft δ ss -perfect ringprojective δ ss-coverprimary 16d1016d60 secondary 16d99 |
| spellingShingle | Türkmen Burcu Nişancı Türkmen Ergül δss-supplemented modules and rings Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica semisimple module strongly δ-local module δ ss -supplemented module left δ ss -perfect ring projective δ ss-cover primary 16d10 16d60 secondary 16d99 |
| title | δss-supplemented modules and rings |
| title_full | δss-supplemented modules and rings |
| title_fullStr | δss-supplemented modules and rings |
| title_full_unstemmed | δss-supplemented modules and rings |
| title_short | δss-supplemented modules and rings |
| title_sort | δss supplemented modules and rings |
| topic | semisimple module strongly δ-local module δ ss -supplemented module left δ ss -perfect ring projective δ ss-cover primary 16d10 16d60 secondary 16d99 |
| url | https://doi.org/10.2478/auom-2020-0041 |
| work_keys_str_mv | AT turkmenburcunisancı dsssupplementedmodulesandrings AT turkmenergul dsssupplementedmodulesandrings |