Minimal abelian varieties of algebras, I
Keith A. Kearnes, Emil W. Kiss, Agnes Szendrei

TL;DR
This paper proves that non-affine abelian varieties always contain a nontrivial strongly abelian subvariety, providing foundational insight for future research on minimal abelian varieties.
Contribution
It establishes a key structural property of non-affine abelian varieties, advancing the understanding of their subvariety composition.
Findings
Non-affine abelian varieties have nontrivial strongly abelian subvarieties.
The result sets the stage for studying minimal abelian varieties in subsequent work.
Abstract
We show that any abelian variety that is not affine has a nontrivial strongly abelian subvariety. In later papers in this sequence we apply this result to the study of minimal abelian varieties.
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