4 citations · 7 across the 6 of their papers we have counts for
7 papers · 1 filter
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…
Modules over trusses vs modules over rings: direct sums and free modules
Tomasz Brzeziński, Bernard Rybołowicz
Categorical constructions on heaps and modules over trusses are considered and contrasted with the corresponding constructions on groups and rings. These include explicit descripti…
Trusses: Paragons, ideals and modules
Tomasz Brzeziński
Trusses, defined as sets with a suitable ternary and a binary operations, connected by the distributive laws, are studied from a ring and module theory point of view. The notions o…
Towards semi-trusses
Tomasz Brzeziński
A general or truss distributive laws between two associative operations on the same set are studied for cancellative and inverse semigroups.
Skew derivations on down-up algebras
Munerah Almulhem, Tomasz Brzeziński
A class of skew derivations on complex Noetherian generalized down-up algebras is constructed.