Generalized “stacked bases” theorem for modules over semiperfect rings

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

In: Communications in Algebra, Vol. 49, No. 6, 10.02.2021, p. 2597-2605.

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

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.

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