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Periodic rings with finitely generated underlying group. (English) Zbl 1120.16303
Summary: We study periodic rings that are finitely generated as groups. We prove several structure results. We classify periodic rings that are free of rank at most 2, and also periodic rings $$R$$ such that $$R$$ is finitely generated as a group and $$R/t(R)\simeq\mathbb Z$$. In this way, we construct new classes of periodic rings. We also ask a question concerning the connection to periodic rings that are finitely generated as rings.
##### MSC:
 16U80 Generalizations of commutativity (associative rings and algebras) 16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) 16P10 Finite rings and finite-dimensional associative algebras
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