Quasi-unit regularity and QB-rings
Some relations for quasiunit regular rings and QB-rings, as well as for pseudounit regular rings and QB ∞-rings, are obtained. In the first part of the paper, we prove that (an exchange ring R is a QB-ring) ⟺ (whenever x ∈ R is regular, there exists a quasiunit regular element w ∈ R such that x = xy...
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| Date: | 2012 |
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Інститут математики НАН України
2012
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| Series: | Український математичний журнал |
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/164158 |
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| Cite this: | Quasi-unit regularity and QB-rings/ Jianghua Li, Xiaoqing Sun, Xiaoqin Shen, Shangping Wang // Український математичний журнал. — 2012. — Т. 64, № 3. — С. 415-425. — Бібліогр.: 9 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1641582025-02-09T12:05:30Z Quasi-unit regularity and QB-rings Квазiодинична регулярнiсть та QB-кiльця Jianghua Li Xiaoqing Sun Xiaoqin Shen Shangping Wang Статті Some relations for quasiunit regular rings and QB-rings, as well as for pseudounit regular rings and QB ∞-rings, are obtained. In the first part of the paper, we prove that (an exchange ring R is a QB-ring) ⟺ (whenever x ∈ R is regular, there exists a quasiunit regular element w ∈ R such that x = xyx = xyw for some y ∈ R) ⟺ (whenever aR + bR = dR in R; there exists a quasiunit regular element w ∈ R such that a + bz = dw for some z ∈ R). Similarly, we also give necessary and sufficient conditions for QB ∞-rings in the second part of the paper. Отримано деякi спiввiдношення для квазiодиничних регулярних кiлець та QB-кiлець, а також для псевдоодиничних регулярних кiлець та QB∞-кiлець. У першiй частинi статтi доведено, що (кiльце R з властивiстю замiни є QB-кiльцем) ⇔ (якщо x∈R є регулярним, то iснує квазiодиничний регулярний елемент w∈R такий, що x=xyx=xyw для деякого y∈R) ⇔ (якщо aR+bR=dR in R в R, то iснує квазiодиничний регулярний елемент w∈R такий, що a+bz=dw для деякого z∈R). Аналогiчним чином отриманi необхiднi та достатнi умови для QB∞-кiлець наведено у другiй частинi статтi. This paper is supported by National Nature Science Foundation of China (NSFC 61173192, 11101330) and Natural Science Foundation of Shaanxi Province (2011JQ1007) and Education Office Foundation of Shaanxi Province (2010JK728) and The Starting Research Fund from Xi’an University of Technology (108-211105). 2012 Article Quasi-unit regularity and QB-rings/ Jianghua Li, Xiaoqing Sun, Xiaoqin Shen, Shangping Wang // Український математичний журнал. — 2012. — Т. 64, № 3. — С. 415-425. — Бібліогр.: 9 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/164158 512.5 en Український математичний журнал application/pdf Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Статті Статті |
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Статті Статті Jianghua Li Xiaoqing Sun Xiaoqin Shen Shangping Wang Quasi-unit regularity and QB-rings Український математичний журнал |
| description |
Some relations for quasiunit regular rings and QB-rings, as well as for pseudounit regular rings and QB ∞-rings, are obtained. In the first part of the paper, we prove that (an exchange ring R is a QB-ring) ⟺ (whenever x ∈ R is regular, there exists a quasiunit regular element w ∈ R such that x = xyx = xyw for some y ∈ R) ⟺ (whenever aR + bR = dR in R; there exists a quasiunit regular element w ∈ R such that a + bz = dw for some z ∈ R). Similarly, we also give necessary and sufficient conditions for QB ∞-rings in the second part of the paper. |
| format |
Article |
| author |
Jianghua Li Xiaoqing Sun Xiaoqin Shen Shangping Wang |
| author_facet |
Jianghua Li Xiaoqing Sun Xiaoqin Shen Shangping Wang |
| author_sort |
Jianghua Li |
| title |
Quasi-unit regularity and QB-rings |
| title_short |
Quasi-unit regularity and QB-rings |
| title_full |
Quasi-unit regularity and QB-rings |
| title_fullStr |
Quasi-unit regularity and QB-rings |
| title_full_unstemmed |
Quasi-unit regularity and QB-rings |
| title_sort |
quasi-unit regularity and qb-rings |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| topic_facet |
Статті |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/164158 |
| citation_txt |
Quasi-unit regularity and QB-rings/ Jianghua Li, Xiaoqing Sun, Xiaoqin Shen, Shangping Wang // Український математичний журнал. — 2012. — Т. 64, № 3. — С. 415-425. — Бібліогр.: 9 назв. — англ. |
| series |
Український математичний журнал |
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| first_indexed |
2025-11-25T22:57:34Z |
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2025-11-25T22:57:34Z |
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