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 …

It is shown that there is a close relationship between ideal extensions of rings and trusses,
that is, sets with a semigroup operation distributing over a ternary abelian heap operation …

Categorical aspects of the theory of modules over trusses are studied. Tensor product of
modules over trusses is defined and its existence established. In particular, it is shown that …

Two observations in support of the thesis that trusses are inherent in ring theory are made.
First, it is shown that every equivalence class of a congruence relation on a ring or …

We examine the heap of linear connections on anchored vector bundles and Lie algebroids.
Naturally, this covers the example of affine connections on a manifold. We present some …

It is shown that the Baer–Kaplansky Theorem can be extended to all abelian groups
provided that the rings of endomorphisms of groups are replaced by trusses of …

The main purpose of this work is to build a refinement of Grigoriev's framework that records
the valuations of the coefficients in a power series solution so that convergence information …

The distributive laws of ring theory are fundamental equalities in algebra. However, recently
in the study of the Yang-Baxter equation, many algebraic structures with alternative …

Connections between heaps of modules and (affine) modules over rings are explored. This
leads to explicit, often constructive, descriptions of some categorical constructions and …

arXiv:2405.02540v1 [math.RT] 4 May 2024 Page 1 arXiv:2405.02540v1 [math.RT] 4 May 2024
Several results on exact sequences in categories of modules over trusses Yongduo Wang∗ …