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Generalized “stacked bases” theorem for modules over semiperfect rings. / Generalov, A. I.; Zilberbord, I. M.

в: Communications in Algebra, Том 49, № 6, 10.02.2021, стр. 2597-2605.

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Generalov, A. I. ; Zilberbord, I. M. / Generalized “stacked bases” theorem for modules over semiperfect rings. в: Communications in Algebra. 2021 ; Том 49, № 6. стр. 2597-2605.

BibTeX

@article{9e7e6cd391cb4a6eb7ac62de7be16ef6,
title = "Generalized “stacked bases” theorem for modules over semiperfect rings",
abstract = "The history of generalized “stacked bases” theorem origins from the result of Hill and Megibben on abelian groups. We extend this theorem for modules over semiperfect rings and as a consequence we show that for a submodule H of a projective module G over a semiperfect ring, the following conditions are equivalent: there exists a decomposition (Formula presented.) into a direct sum of indecomposable modules Pi, such that (Formula presented.) G/H is a direct sum of a family of modules, isomorphic to factor modules of principal indecomposable modules.",
keywords = "Principal indecomposable module, projective module, semiperfect ring, stacked basis, stacked decomposition, direct sum decomposition and cancellation in associative algebras, bimodules and ideals",
author = "Generalov, {A. I.} and Zilberbord, {I. M.}",
note = "Publisher Copyright: {\textcopyright} 2021 Taylor & Francis Group, LLC.",
year = "2021",
month = feb,
day = "10",
doi = "10.1080/00927872.2021.1879105",
language = "English",
volume = "49",
pages = "2597--2605",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor & Francis",
number = "6",

}

RIS

TY - JOUR

T1 - Generalized “stacked bases” theorem for modules over semiperfect rings

AU - Generalov, A. I.

AU - Zilberbord, I. M.

N1 - Publisher Copyright: © 2021 Taylor & Francis Group, LLC.

PY - 2021/2/10

Y1 - 2021/2/10

N2 - The history of generalized “stacked bases” theorem origins from the result of Hill and Megibben on abelian groups. We extend this theorem for modules over semiperfect rings and as a consequence we show that for a submodule H of a projective module G over a semiperfect ring, the following conditions are equivalent: there exists a decomposition (Formula presented.) into a direct sum of indecomposable modules Pi, such that (Formula presented.) G/H is a direct sum of a family of modules, isomorphic to factor modules of principal indecomposable modules.

AB - The history of generalized “stacked bases” theorem origins from the result of Hill and Megibben on abelian groups. We extend this theorem for modules over semiperfect rings and as a consequence we show that for a submodule H of a projective module G over a semiperfect ring, the following conditions are equivalent: there exists a decomposition (Formula presented.) into a direct sum of indecomposable modules Pi, such that (Formula presented.) G/H is a direct sum of a family of modules, isomorphic to factor modules of principal indecomposable modules.

KW - Principal indecomposable module

KW - projective module

KW - semiperfect ring

KW - stacked basis

KW - stacked decomposition

KW - direct sum decomposition and cancellation in associative algebras

KW - bimodules and ideals

UR - http://www.scopus.com/inward/record.url?scp=85101057077&partnerID=8YFLogxK

U2 - 10.1080/00927872.2021.1879105

DO - 10.1080/00927872.2021.1879105

M3 - Article

AN - SCOPUS:85101057077

VL - 49

SP - 2597

EP - 2605

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 6

ER -

ID: 73698157