16 citations · 27 across the 5 of their papers we have counts for
8 papers
Boolean Trusses as Rectangular Bands and Boolean Rings
Ryszard R. Andruszkiewicz, Bernard Rybołowicz
We introduce Boolean trusses, that is, trusses in which every element is idempotent. Every Boolean truss admits a decomposition into a truss arising from a Boolean ring and a recta…
Heaps of modules: Categorical aspects
Simion Breaz, Tomasz Brzezinski, Bernard Rybolowicz +1
Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and pr…
Heaps of modules and affine spaces
Simion Breaz, Tomasz Brzeziński, Bernard Rybołowicz +1
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 deriv…
Ideal ring extensions and trusses
Ryszard R. Adruszkiewicz, Tomasz Brzeziński, Bernard Rybołowicz
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 oper…
From pre-trusses to skew braces
Tomasz Brzeziński, Stefano Mereta, Bernard Rybołowicz
The notion of a pre-truss, that is, a set that is both a heap and a semigroup is introduced. Pre-trusses themselves as well as pre-trusses in which one-sided or two-sided distribut…
On functors between categories of modules over trusses
Tomasz Brzeziński, Bernard Rybołowicz, Paolo Saracco
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 t…