In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-lik...

The results of J. F. Qian et al. [5] on (1 − γ)-constacyclic codes over finite chain rings of nilpotency index 2 are extended to (1 − γe)constacyclic codes over finite chain rings of arbitrary nilpotency index e+1. The Gray map is introduced for this type of rings. We prove that the Gray image of a linear (1− γe)-constacyclic code over a finite chain ring is a distance-invariant quasi-cyclic co...

We call (i?) 1 the Lie ring associated with R, and denote it by 9Î. The question of how far the properties of SR determine those of R is of considerable interest, and has been studied extensively for the case when R is an algebra, but little is known of the situation in general. In an earlier paper the author investigated the effect of the nilpotency of 9î upon the structure of R if R contains ...

This research was motivated by universal algebraic geometry. One of the central questions of universal algebraic geometry is: when two algebras have the same algebraic geometry? For answer of this question (see [8],[10]) we must consider the variety Θ, to which our algebras belongs, the category Θ of all finitely generated free algebras of Θ and research how the group AutΘ of all the automorphi...

In this paper, we prove that maximal (k, 2)-arcs in projective Hjelmslev planes over chain rings R of nilpotency index 2 exist if and only if charR = 4. © 2005 Elsevier Inc. All rights reserved.

SUANMALI, SUTHATHIP. On the Relationship between the Class of a Lie Algebra and the Classes of its Subalgebras. (Under the direction of Ernie L. Stitzinger.) A classical nilpotency result considers finite p-groups whose proper subgroups all have class bounded by a fixed number n. We consider the analogous property in nilpotent Lie algebras. In particular, we investigate whether this condition p...