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  • Thesis

  • Authors: Gouraige, Rony (2006)

  • Two elements in a finite-dimensional central simple algebra are said to be z-equivalent if the corresponding centralizers are conjugate. We determine in this thesis the invariants which characterize z-equivalence.

  • Thesis

  • Authors: Desai, Angela (2006)

  • In this paper we discuss subsystem and coding results in Zd symbolic dynamics for d > 1. We prove that any Zd shift of finite type with positive topological entropy has a family of subsystems of finite type whose entropies are dense in the interval from zero to the entropy of the original shift. We show a similar result for Zd sofic shifts, and also show every Zd sofic shift can be covered by a Zd shift of finite type arbitrarily close in entropy. We also show that if a Z2 shift of finite type with entropy greater than log N satisfies a certain mixing condition, then it must factor onto the full N-shift.