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Strongly solvable varieties

  • Ralph McKenzie
  • Matthew Valeriote
Chapter
Part of the Progress in Mathematics book series (PM, volume 79)

Abstract

The plan of Part II is as follows. We deal with a locally finite, structured, Abelian variety V. According to Theorem 1.3, we have V = V1 V V2 where V1 and V2 are the sub varieties of V that are defined in Definition 1.1. The first principal result of Part II is achieved in Theorem 9.6: V1 is strongly Abelian and V2 is affine. The second principal result is Theorem 11.9: V1 is equivalent to a structured variety of multi-sorted unary algebras. The third principal result is Theorem 12.19, which characterizes the decidable, locally finite, strongly solvable varieties in terms of an elementary property of the associated variety of multi-sorted unary algebras.

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Copyright information

© Birkhäuser Boston, Inc. 1989

Authors and Affiliations

  • Ralph McKenzie
    • 1
  • Matthew Valeriote
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

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