Об одном обобщении самоинъективных колец

Translated title of the contribution: On a generalization of self-injective rings

И.М. Зильберборд, С.В. Сотников

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Translated title of the contributionOn a generalization of self-injective rings
Original languageRussian
Pages (from-to)60-68
Number of pages9
JournalВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ
Volume7(65)
Issue number1
StatePublished - Mar 2020

Scopus subject areas

  • Mathematics(all)

Keywords

  • injective module
  • semisimple module
  • self-injective ring
  • Peirce decomposition

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