let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...

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...

High-speed links which employ source synchronous clocking architectures have the ability to track correlated jitter between clock and data channels up to high frequencies. However, system timing margins are degraded by channel skew between clock and data signals and high-frequency loss. This paper describes how these key channel effects impact the jitter performance and influence the clocking a...

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...