On a Generalization of Self-Injective Rings

I. M. Zilberbord, S. V. Sotnikov

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)45-51
Число страниц7
ЖурналVestnik St. Petersburg University: Mathematics
Том53
Номер выпуска1
DOI
СостояниеОпубликовано - 1 янв 2020

Предметные области Scopus

  • Математика (все)

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