Algebraic Properties of Semi-Direct Sums of Rings
Let R be an associative ring not necessarily with unity. We say that R is a semi-direct sum of rings S and I, if R = S + I, where S is a subring of a ring R, I is an ideal of R and S ∩ I = {0}.
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| Format: | Article |
| Language: | English |
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Sciendo
2025-06-01
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| Series: | Annales Mathematicae Silesianae |
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| Online Access: | https://doi.org/10.2478/amsil-2025-0012 |
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| _version_ | 1849316994362376192 |
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| author | Nowakowska Marta |
| author_facet | Nowakowska Marta |
| author_sort | Nowakowska Marta |
| collection | DOAJ |
| description | Let R be an associative ring not necessarily with unity. We say that R is a semi-direct sum of rings S and I, if R = S + I, where S is a subring of a ring R, I is an ideal of R and S ∩ I = {0}. |
| format | Article |
| id | doaj-art-71e75f89361c43ccb10e0e3f5d49c362 |
| institution | Kabale University |
| issn | 2391-4238 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj-art-71e75f89361c43ccb10e0e3f5d49c3622025-08-20T03:51:24ZengSciendoAnnales Mathematicae Silesianae2391-42382025-06-0139231933010.2478/amsil-2025-0012Algebraic Properties of Semi-Direct Sums of RingsNowakowska Marta0University of Silesia in Katowice, Katowice, PolandLet R be an associative ring not necessarily with unity. We say that R is a semi-direct sum of rings S and I, if R = S + I, where S is a subring of a ring R, I is an ideal of R and S ∩ I = {0}.https://doi.org/10.2478/amsil-2025-001216l3016n2016s7016s99semi-direct sumamalgamated ringjacobson radicalleft steinitz ringuniquely clean ringlocal ring |
| spellingShingle | Nowakowska Marta Algebraic Properties of Semi-Direct Sums of Rings Annales Mathematicae Silesianae 16l30 16n20 16s70 16s99 semi-direct sum amalgamated ring jacobson radical left steinitz ring uniquely clean ring local ring |
| title | Algebraic Properties of Semi-Direct Sums of Rings |
| title_full | Algebraic Properties of Semi-Direct Sums of Rings |
| title_fullStr | Algebraic Properties of Semi-Direct Sums of Rings |
| title_full_unstemmed | Algebraic Properties of Semi-Direct Sums of Rings |
| title_short | Algebraic Properties of Semi-Direct Sums of Rings |
| title_sort | algebraic properties of semi direct sums of rings |
| topic | 16l30 16n20 16s70 16s99 semi-direct sum amalgamated ring jacobson radical left steinitz ring uniquely clean ring local ring |
| url | https://doi.org/10.2478/amsil-2025-0012 |
| work_keys_str_mv | AT nowakowskamarta algebraicpropertiesofsemidirectsumsofrings |