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On a Generalization of Self-Injective Rings. / Zilberbord, I. M.; Sotnikov, S. V.

In: Vestnik St. Petersburg University: Mathematics, Vol. 53, No. 1, 01.01.2020, p. 45-51.

Research output: Contribution to journal › Article › peer-review

Harvard

Zilberbord, IM & Sotnikov, SV 2020, 'On a Generalization of Self-Injective Rings', Vestnik St. Petersburg University: Mathematics, vol. 53, no. 1, pp. 45-51. https://doi.org/10.1134/S106345412001015X

APA

Zilberbord, I. M., & Sotnikov, S. V. (2020). On a Generalization of Self-Injective Rings. Vestnik St. Petersburg University: Mathematics, 53(1), 45-51. https://doi.org/10.1134/S106345412001015X

Vancouver

Zilberbord IM, Sotnikov SV. On a Generalization of Self-Injective Rings. Vestnik St. Petersburg University: Mathematics. 2020 Jan 1;53(1):45-51. https://doi.org/10.1134/S106345412001015X

Author

Zilberbord, I. M. ; Sotnikov, S. V. / On a Generalization of Self-Injective Rings. In: Vestnik St. Petersburg University: Mathematics. 2020 ; Vol. 53, No. 1. pp. 45-51.

BibTeX

@article{490831e58afe4aaeb59d50106fbb27fc,
title = "On a Generalization of Self-Injective Rings",
abstract = "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.",
keywords = "injective module, Peirce decomposition, self-injective ring, semisimple module",
author = "Zilberbord, {I. M.} and Sotnikov, {S. V.}",
note = "Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = jan,
day = "1",
doi = "10.1134/S106345412001015X",
language = "English",
volume = "53",
pages = "45--51",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - On a Generalization of Self-Injective Rings

AU - Zilberbord, I. M.

AU - Sotnikov, S. V.

N1 - Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - injective module

KW - Peirce decomposition

KW - self-injective ring

KW - semisimple module

UR - http://www.scopus.com/inward/record.url?scp=85082605760&partnerID=8YFLogxK

U2 - 10.1134/S106345412001015X

DO - 10.1134/S106345412001015X

M3 - Article

AN - SCOPUS:85082605760

VL - 53

SP - 45

EP - 51

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 71671848