For k a field of arbitrary characteristic, and R a k-algebra, we show that the PI degree of an iterated skew polynomial ring R[x1; τ1, δ1] · · · [xn; τn, δn] agrees with the PI degree of R[x1; τ1] · · · [xn; τn] when each (τi, δi) satisfies a qi-skew relation for qi ∈ k and extends to a higher qi-skew τi-derivation. We confirm the quantum Gel’fand-Kirillov conjecture for various quantized coord...

We introduce circulant matrices that capture the structure of a skew-polynomial ring F[x; θ] modulo the left ideal generated by a polynomial of the type x − a. This allows us to develop an approach to skew-constacyclic codes based on such circulants. Properties of these circulants are derived, and in particular it is shown that the transpose of a certain circulant is a circulant again. This rec...

Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation. To study non-involutive solutions one needs skew braces, a non-commutative analog of braces. In this talk we discuss basic properties of skew braces and how these structures are related to the Yang-Baxter equation. We also discuss interesting connections between skew braces and...

We design a non-commutative version of the Peterson-Gorenstein-Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In p...

Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B := A[[y;α]] 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.

A number of results are proved concerning the Quillen ^-theory K+(S*G) of the skew group ring S*G, where S is a Noetherian ring and G is a finite group of automorphisms of 5. Applications are given to the computation of AT-groups of group algebras and of equivariant /^-theory for affine varieties.

We describe a high performance clocking methodology for domino pipelines. Our technique maximizes the clock rate of the circular pipeline (“ring”) while maintaining the ring cycle time to be the worst-case combinational logic delay around the ring. It is relatively immune to global clock skew, incurs no latch overhead, allows up to 50% time borrowing, and offers a robust way of preventing race-...

Alonso P. Moreno, Viviana M. Berthoud, Gregorio Pérez-Palacios, and E. Martha Pérez-Armendariz Krannert Institute of Cardiology, Indiana School of Medicine, Indianapolis, Indiana; Section of Hematology/Oncology, Department of Pediatrics, University of Chicago, Chicago, Illinois; and Facultad de Medicina, Departmento de Medicina Experimental, Unidad de Investigación, Enseñanza y Comunicación Ens...