2016/12/28 by Bavula, V. V · 1 citation
#16D25 #16D30 #16P40 #16P50 #16S85 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1612.08941
The aim of the paper is to extend the class of generalized Weyl algebras to a larger class of rings (they are also called \em generalized Weyl algebras) that are determined by two ring endomorphisms rather than one as in the case of `old' GWAs. A new class of rings, the \em diskew polynomial rings, is introduced that is closely related to GWAs (they are GWAs under a mild condition). The, so-called, ambiskew polynomial rings are a small subclass of the class of diskew polynomial rings. Semisimplicity criteria are given for generalized Weyl algebras and diskew polynomial rings.