Hilbert's Theorem 90 in monoidal categories

A. Al-Rawashdeh; B. Mesablishvili

doi:10.1016/j.jalgebra.2022.02.013

Hilbert's Theorem 90 in monoidal categories

A. Al-Rawashdeh, B. Mesablishvili

Department of Mathematical Sciences

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

Abstract

A categorified version of Hilbert's Theorem 90 is given. The natural setting for our result is that of symmetric monoidal categories. Some applications to the symmetric monoidal categories of modules over a commutative ring, chain complexes and Banach spaces are given.

Original language	English
Pages (from-to)	1-36
Number of pages	36
Journal	Journal of Algebra
Volume	602
DOIs	https://doi.org/10.1016/j.jalgebra.2022.02.013
Publication status	Published - Jul 15 2022

Keywords

(Co)algebras in a monoidal category
Banach spaces
Chain complexes
Descent cohomology
Galois extensions
Hilbert's Theorem 90
Monoidal categories

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2022.02.013

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title = "Hilbert's Theorem 90 in monoidal categories",

abstract = "A categorified version of Hilbert's Theorem 90 is given. The natural setting for our result is that of symmetric monoidal categories. Some applications to the symmetric monoidal categories of modules over a commutative ring, chain complexes and Banach spaces are given.",

keywords = "(Co)algebras in a monoidal category, Banach spaces, Chain complexes, Descent cohomology, Galois extensions, Hilbert's Theorem 90, Monoidal categories",

author = "A. Al-Rawashdeh and B. Mesablishvili",

note = "Funding Information: The authors acknowledge with thanks the Department of Research Affairs at UAEU. This project is supported by the Post-Doc Grant (2019), Fund No. 31S404. Funding Information: The authors acknowledge with thanks the Department of Research Affairs at UAEU . This project is supported by the Post-Doc Grant (2019), Fund No. 31S404 . Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

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AU - Mesablishvili, B.

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N2 - A categorified version of Hilbert's Theorem 90 is given. The natural setting for our result is that of symmetric monoidal categories. Some applications to the symmetric monoidal categories of modules over a commutative ring, chain complexes and Banach spaces are given.

AB - A categorified version of Hilbert's Theorem 90 is given. The natural setting for our result is that of symmetric monoidal categories. Some applications to the symmetric monoidal categories of modules over a commutative ring, chain complexes and Banach spaces are given.

KW - (Co)algebras in a monoidal category

KW - Banach spaces

KW - Chain complexes

KW - Descent cohomology

KW - Galois extensions

KW - Hilbert's Theorem 90

KW - Monoidal categories

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VL - 602

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EP - 36

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Hilbert's Theorem 90 in monoidal categories

Abstract

Keywords

ASJC Scopus subject areas

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