Dimension Theory in Iterated Local Skew Power Series Rings

Abstract Many well-known local rings, including soluble Iwasawa algebras and certain completed quantum algebras, arise naturally as iterated skew power series rings. We calculate their Krull global dimensions, obtaining lower bounds to complement the upper obtained by Wang. In fact, we show that many common such rings obey a stronger property, which call triangularity, allows us also classical dimension (prime length). Finally, correct an error in literature regarding associated graded of general but triangularity is enough recover this result.