Heaps of modules and affine spaces

TL;DR

This paper introduces heaps of modules as an affine generalization of modules over rings or trusses, exploring their properties, examples from geometry and topology, and their relationships with classical algebraic structures.

Contribution

It defines and studies heaps of modules, establishing their properties, providing geometric and topological examples, and analyzing their connections to traditional modules and affine spaces.

Findings

Heaps of modules generalize modules over rings and trusses.

Examples include affine spaces and chain contractions in topology.

Relationships between heaps of modules and classical algebraic structures are clarified.

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 and modules over a ring and affine spaces are revealed and analysed.