Heaps of modules and affine spaces

Simion Breaz; Tomasz Brzeziński; Bernard Rybołowicz; Paolo Saracco

doi:10.1007/s10231-023-01369-0

Heaps of modules and affine spaces

Simion Breaz, Tomasz Brzeziński, Bernard Rybołowicz^*, Paolo Saracco

^*Corresponding author for this work

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6 Citations (Scopus)

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Abstract

A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine spaces) and algebraic topology (chain contractions) are presented. Relationships between heaps of modules, modules over a ring and affine spaces are revealed and analysed.

Original language	English
Pages (from-to)	403-445
Number of pages	43
Journal	Annali di Matematica Pura ed Applicata
Volume	203
Early online date	30 Aug 2023
DOIs	https://doi.org/10.1007/s10231-023-01369-0
Publication status	Published - Feb 2024

Keywords

Affine geometry
Modules over rings
Modules over trusses
16S70
14R20
20N10
16Y99
08A99

ASJC Scopus subject areas

Applied Mathematics

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title = "Heaps of modules and affine spaces",

abstract = "A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine spaces) and algebraic topology (chain contractions) are presented. Relationships between heaps of modules, modules over a ring and affine spaces are revealed and analysed.",

keywords = "Affine geometry, Modules over rings, Modules over trusses, 16S70, 14R20, 20N10, 16Y99, 08A99",

author = "Simion Breaz and Tomasz Brzezi{\'n}ski and Bernard Rybo{\l}owicz and Paolo Saracco",

note = "Funding Information: The research of S. Breaz is supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI–UEFISCDI, project number PN-III-P4-ID-PCE-2020-0454, within PNCDI III. Funding Information: The research of B. Rybo{\l}owicz is supported by the EPSRC grant EP/V008129/1. Funding Information: The research of T. Brzezi{\'n}ski is partially supported by the National Science Centre, Poland, grant no. 2019/35/B/ST1/01115. Publisher Copyright: {\textcopyright} 2023, The Author(s).",

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doi = "10.1007/s10231-023-01369-0",

language = "English",

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AU - Breaz, Simion

AU - Brzeziński, Tomasz

AU - Rybołowicz, Bernard

AU - Saracco, Paolo

N1 - Funding Information: The research of S. Breaz is supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI–UEFISCDI, project number PN-III-P4-ID-PCE-2020-0454, within PNCDI III. Funding Information: The research of B. Rybołowicz is supported by the EPSRC grant EP/V008129/1. Funding Information: The research of T. Brzeziński is partially supported by the National Science Centre, Poland, grant no. 2019/35/B/ST1/01115. Publisher Copyright: © 2023, The Author(s).

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N2 - A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine spaces) and algebraic topology (chain contractions) are presented. Relationships between heaps of modules, modules over a ring and affine spaces are revealed and analysed.

AB - A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine spaces) and algebraic topology (chain contractions) are presented. Relationships between heaps of modules, modules over a ring and affine spaces are revealed and analysed.

KW - Affine geometry

KW - Modules over rings

KW - Modules over trusses

KW - 16S70

KW - 14R20

KW - 20N10

KW - 16Y99

KW - 08A99

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DO - 10.1007/s10231-023-01369-0

M3 - Article

AN - SCOPUS:85169592243

SN - 0373-3114

VL - 203

SP - 403

EP - 445

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

ER -

Heaps of modules and affine spaces

Abstract

Keywords

ASJC Scopus subject areas

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