Projective discrete modules over profinite groups

Alexandru Chirvasitu; Ryo Kanda

doi:10.1016/j.jpaa.2022.107260

Projective discrete modules over profinite groups

Alexandru Chirvasitu
, Ryo Kanda

Mathematics

Osaka Metropolitan University

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

2 Scopus citations

Abstract

We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology.

Original language	English
Article number	107260
Journal	Journal of Pure and Applied Algebra
Volume	227
Issue number	4
DOIs	https://doi.org/10.1016/j.jpaa.2022.107260
State	Published - Apr 2023

Keywords

Abelian category
Discrete module
Grothendieck category
Linear topology
Profinite group
Projective object

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10.1016/j.jpaa.2022.107260

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title = "Projective discrete modules over profinite groups",

abstract = "We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology.",

keywords = "Abelian category, Discrete module, Grothendieck category, Linear topology, Profinite group, Projective object",

author = "Alexandru Chirvasitu and Ryo Kanda",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2023",

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doi = "10.1016/j.jpaa.2022.107260",

language = "English",

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AU - Chirvasitu, Alexandru

AU - Kanda, Ryo

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N2 - We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology.

AB - We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology.

KW - Abelian category

KW - Discrete module

KW - Grothendieck category

KW - Linear topology

KW - Profinite group

KW - Projective object

UR - https://www.scopus.com/pages/publications/85141982391

U2 - 10.1016/j.jpaa.2022.107260

DO - 10.1016/j.jpaa.2022.107260

M3 - Article

AN - SCOPUS:85141982391

SN - 0022-4049

VL - 227

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 4

M1 - 107260

ER -

Projective discrete modules over profinite groups

Abstract

Keywords

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