19 citations · 95 across the 22 of their papers we have counts for
34 papers
Comparing self-dual corings, Frobenius corings and Ringel self-duality
Tomasz Brzeziński, Teresa Conde, Steffen Koenig +1
Self-dual corings and self-dual algebra extensions are classified and these (self-)dualities are compared with Ringel (self-)duality, revealing fundamental differences. To each cor…
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…
The Baer-Kaplansky theorem for all abelian groups and modules
Simion Breaz, Tomasz Brzeziński
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 endomorphisms of cor…
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…
An algebraic framework for noncommutative bundles with homogeneous fibres
Tomasz Brzeziński, Wojciech Szymański
An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the ro…