title: On a generalization of self-injective rings
metadata.name: dc.contributor.author
metadata.value: Zilberbord, Igor M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Sotnikov, Sergei V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T12:33:07Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:33:07Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zilberbord I.M., Sotnikov S.V. On a generalization of self-injective rings. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 60–68.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.106
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17328
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this work the notion of left (right) self-injective ring is generalized. We consider rings
  that are direct sum of injective module and semisimple module as a left (respectively,
  right) module above itself. We call such rings left (right) semi-injective and research their
  properties with the help of two-sided Peirce decomposition of the ring. The paper contains
  the description of left Noetherian left semi-injective rings. It is proved that any such ring
  is a direct product of (two-sided) self-injective ring and several quotient rings (of special
  kind) of rings of upper-triangular matrices over skew fields. From this description it follows
  that for left semi-injective rings we have the analogue of the classical result for self-injective
  rings. Namely, if a ring is left Noetherian and left semi-injective then this ring is also right
  semi-injective and two-sided Artinian.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: injective module
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: semisimple module
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: self-injective ring
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Peirce decomposition
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On a generalization of self-injective rings
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 60-68.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17328/1/60-68.pdf
resources.format: Adobe PDF
resources.size: 290,85 kB