Structure of Decidable Locally Finite Varieties pp 103-105 | Cite as

# Consequences of the transfer principles

Chapter

## Abstract

Throughout this chapter we assume that *V* is a locally finite Abelian variety. We will show that if *V* satisfies the (**1,2**) transfer principle, then the subvariety *V*_{1} = * V*(

*S*

_{1}) defined in Chapter 1 is strongly Abelian. On the other hand, if

*V*is assumed to satisfy the (

**2,1**) transfer principle, then it will be shown that the subvariety

*V*

_{2}=

*(*

**V***S*

_{2}) is affine. Thus if

*V*is structured, then we will be able to conclude with the help of Theorem 8.9 and Theorem 1.3 that

*V*is the join of an affine subvariety with a strongly Abelian one.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Birkhäuser Boston, Inc. 1989