Rings with finite decomposition of identity
A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semid...
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| Published in: | Український математичний журнал |
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| Date: | 2011 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2011
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| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/166010 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Rings with finite decomposition of identity / M.A. Dokuchaev, N.M. Gubareni, V.V. Kirichenko // Український математичний журнал. — 2011. — Т. 63, № 3. — С. 319–340. — Бібліогр.: 48 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semidistributive semiperfect ring is distributive. An application of decompositions of identity to groups of units is given.
Наведено критерiй первинностi напiвпервинних кiлець iз скiнченним розкладом одиницi, а також короткий огляд деяких умов скiнченностi вiдносно розкладу одиницi. Розглянуто поняття сiтки кiльця i показано, що решiтка всiх двобiчних iдеалiв правого напiвдистрибутивного напiвдосконалого кiльця є дистрибутивною. Наведено застосування розкладу одиницi до груп одиниць.
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| ISSN: | 1027-3190 |