9 citations · 13 across the 7 of their papers we have counts for
7 papers
Involutions in the Cayley-Dickson construction
Masood Aryapoor, Per Bäck, Sophie Pautrel
We determine all involutions in the Cayley-Dickson construction that extend the involution of the original -algebra. We also find all algebra isomorphisms between the resulting…
Hilbert's basis theorem for Poisson Ore extensions
Per Bäck, Patrik Lundström, Johan Öinert +1
We prove an analogue of Hilbert's basis theorem for Poisson Ore extensions and Poisson Laurent Ore extensions. We also obtain corresponding results for iterated Poisson Ore extensi…
The higher-order hom-associative Weyl algebras
Per Bäck
We show that the higher-order Weyl algebras over a field of characteristic zero, which are formally rigid as associative algebras, can be formally deformed in a nontrivial way as h…
Non-associative versions of Hilbert's basis theorem
Per Bäck, Johan Richter
We prove several new versions of Hilbert's basis theorem for non-associative Ore extensions, non-associative skew Laurent polynomial rings, non-associative skew power series rings,…
Flipped non-associative polynomial rings and the Cayley-Dickson construction
Masood Aryapoor, Per Bäck
We introduce and study flipped non-associative polynomial rings. In particular, we show that all Cayley-Dickson algebras naturally appear as quotients of a certain type of such rin…
Simplicity of non-associative skew Laurent polynomial rings
Per Bäck, Johan Richter
We introduce non-associative skew Laurent polynomial rings and characterize when they are simple. Thereby, we generalize results by Jordan, Voskoglou, and Nystedt and Öinert.
Hilbert's basis theorem for non-associative and hom-associative Ore extensions
Per Bäck, Johan Richter
We prove a hom-associative version of Hilbert's basis theorem, which includes as special cases both a non-associative version and the classical associative Hilbert's basis theorem…