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Let A be a semprime, right noetherian ring equipped with an automorphism alpha, and let B := A[[y; alpha]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A and B are equal. We also record applications to induced ideals.
We study prime ideals in skew power series rings $T:=R[[y;tau,delta]]$, for suitably conditioned right noetherian complete semilocal rings $R$, automorphisms $tau$ of $R$, and $tau$-derivations $delta$ of $R$. These rings were introduced by Venjakob,
We study the q-commutative power series ring R:=k_q[[x_1,...,x_n]], defined by the relations x_ix_j = q_{ij}x_j x_i, for multiplicatively antisymmetric scalars q_{ij} in a field k. Our results provide a detailed account of prime ideal structure for a
An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with exponents
We continue the first and second authors study of $q$-commutative power series rings $R=k_q[[x_1,ldots,x_n]]$ and Laurent series rings $L=k_q[[x^{pm 1}_1,ldots,x^{pm 1}_n]]$, specializing to the case in which the commutation parameters $q_{ij}$ are a
We prove that the local components of an automorphic representation of an adelic semisimple group have equal rank in the sense defined earlier by the second author. Our theorem is an analogue of the results previously obtained by Howe, Li, Dvorsky--S