# Dimension Theory in Iterated Local Skew Power Series Rings

@article{Woods2018DimensionTI,
title={Dimension Theory in Iterated Local Skew Power Series Rings},
author={Billy Woods},
journal={Algebras and Representation Theory},
year={2018}
}
• Billy Woods
• Published 26 November 2018
• Mathematics
• Algebras and Representation Theory
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 and global dimensions, obtaining lower bounds to complement the upper bounds obtained by Wang. In fact, we show that many common such rings obey a stronger property, which we call triangularity, and which allows us also to calculate their classical Krull dimension (prime length). Finally, we correct an error in the…
2 Citations
• Mathematics
• 2021
In this paper, we investigate the structure of skew power series rings of the form S = R [[ x ; σ, δ ]], where R is a complete, positively ﬁltered ring and ( σ, δ ) is a skew derivation respecting
• Mathematics
• 2023
Given a complete, positively ﬁltered ring ( R, f ) and a compatible skew derivation ( σ, δ ), we may construct its skew power series ring R [[ x ; σ, δ ]]. Due to topological obstructions, even if δ

## References

SHOWING 1-10 OF 32 REFERENCES

• Mathematics
• 2011
In this paper, we contrast the structure of a noncommutative algebra R with that of the skew power series ring R[[y;d]]. Several of our main results examine when the rings R, Rd, and R[[y;d]] are
• Mathematics
• 2007
This paper is a natural continuation of the study of skew power series rings A initiated in [P. Schneider and O. Venjakob, On the codimension of modules over skew power series rings with applications
• Mathematics
• 2010
This paper is a natural continuation of the study of skew power series rings $A=R[[t;\sigma,\delta]]$ initiated in an earlier work. We construct skew Laurent series rings $B$ and show the existence
• Mathematics
• 2007
We study the “q-commutative” power series ring R: = kq[[x1,...,xn]], defined by the relations xixj = qijxjxi, for mulitiplicatively antisymmetric scalars qij in a field k. Our results provide a
• Mathematics
• 2012
1. General Theory of Primes.- 2. Maximal Orders and Primes.- 3. Extensions of Valuations to some Quantized Algebras
In this paper and a forthcoming joint one with Y. Hachimori we study Iwasawa modules over an infinite Galois extension K of a number field k whose Galois group G=G(K/k) is isomorphic to the
We study prime ideals in skew power series rings T:= R[[y; τ, δ]], for suitably conditioned complete right Noetherian rings R, automorphisms τ of R, and τ-derivations δ of R. Such rings were
• Mathematics
• 2002
We study pre-balanced dualizing complexes over noncommutative complete semilocal algebras and prove an analogue of Van den Bergh’s theorem [VdB, 6.3]. The relationship between pre-balanced dualizing