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arXiv · 1401.1607

Algebras with only finitely many subalgebras

Michiel Kosters
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Abstract

Let R be a commutative ring. A not necessarily commutative R-algebra A is called futile if it has only finitely many R-subalgebras. In this article we relate the notion of futility to familiar properties of rings and modules. We do this by first reducing to the case where A is commutative. Then we refine the description of commutative futile algebras from Dobbs, Picavet and Picavet-L'hermite.

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Michiel Kosters. 2014-01-08. Algebras with only finitely many subalgebras. https://doi.org/10.1142/s0219498815500863

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