Rings decomposed into direct sums of J-rings and nil rings
Let R be a ring (not necessarily with identity) and let E denote the set of idempotents of R. We prove that R is a direct sum of a J-ring (every element is a power of itself) and a nil ring if and only if R is strongly π-regular and E is contained in some J-ideal of R. As a direct consequence of thi...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000230 |
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| _version_ | 1832545669354618880 |
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| author | Hisao Tominaga |
| author_facet | Hisao Tominaga |
| author_sort | Hisao Tominaga |
| collection | DOAJ |
| description | Let R be a ring (not necessarily with identity) and let E denote the set of idempotents of R. We prove that R is a direct sum of a J-ring (every element is a power of itself) and a nil ring if and only if R is strongly π-regular and E is contained in some J-ideal of R. As a direct consequence of this result, the main theorem of [1] follows. |
| format | Article |
| id | doaj-art-bcd728c3d53843459f7f146d7dfdf667 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bcd728c3d53843459f7f146d7dfdf6672025-02-03T07:25:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018120520710.1155/S0161171285000230Rings decomposed into direct sums of J-rings and nil ringsHisao Tominaga0Department of Mathematics, Okayama University, Okayama 700, JapanLet R be a ring (not necessarily with identity) and let E denote the set of idempotents of R. We prove that R is a direct sum of a J-ring (every element is a power of itself) and a nil ring if and only if R is strongly π-regular and E is contained in some J-ideal of R. As a direct consequence of this result, the main theorem of [1] follows.http://dx.doi.org/10.1155/S0161171285000230periodicpotentJ-ringnil ringstrongly π-regular ringdirect sum. |
| spellingShingle | Hisao Tominaga Rings decomposed into direct sums of J-rings and nil rings International Journal of Mathematics and Mathematical Sciences periodic potent J-ring nil ring strongly π-regular ring direct sum. |
| title | Rings decomposed into direct sums of J-rings and nil rings |
| title_full | Rings decomposed into direct sums of J-rings and nil rings |
| title_fullStr | Rings decomposed into direct sums of J-rings and nil rings |
| title_full_unstemmed | Rings decomposed into direct sums of J-rings and nil rings |
| title_short | Rings decomposed into direct sums of J-rings and nil rings |
| title_sort | rings decomposed into direct sums of j rings and nil rings |
| topic | periodic potent J-ring nil ring strongly π-regular ring direct sum. |
| url | http://dx.doi.org/10.1155/S0161171285000230 |
| work_keys_str_mv | AT hisaotominaga ringsdecomposedintodirectsumsofjringsandnilrings |