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

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

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

Generalov, AI & Zilberbord, IM 2021, 'Generalized “stacked bases” theorem for modules over semiperfect rings', *Communications in Algebra*, vol. 49, no. 6, pp. 2597-2605. https://doi.org/10.1080/00927872.2021.1879105

Generalov, A. I., & Zilberbord, I. M. (2021). Generalized “stacked bases” theorem for modules over semiperfect rings. *Communications in Algebra*, *49*(6), 2597-2605. https://doi.org/10.1080/00927872.2021.1879105

Generalov AI, Zilberbord IM. Generalized “stacked bases” theorem for modules over semiperfect rings. Communications in Algebra. 2021 Feb 10;49(6):2597-2605. https://doi.org/10.1080/00927872.2021.1879105

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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",

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AU - Zilberbord, I. M.

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PY - 2021/2/10

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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

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JO - Communications in Algebra

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