Group identities on the units of algebraic algebras with applications to restricted enveloping algebras
classification
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keywords
gi-algebragroupalgebraicalgebraseveryidentityunitsalgebra
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An algebra is called a GI-algebra if its group of units satisfies a group identity. We provide positive support for the following two open problems. 1. Does every algebraic GI-algebra satisfy a polynomial identity? 2. Is every algebraically generated GI-algebra locally finite?
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