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arXiv · 2608.20570

The Parafree Conjecture for associative algebras

Vasily Ionin·Roman Mikhailov
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Abstract

For every base field, we construct a finitely generated parafree augmented associative algebra with countably infinite-dimensional second homology. This disproves the analogue of the Parafree Conjecture for associative algebras and answers a question of Ivanov and Lopatkin. Our example is the monoid algebra of a finitely generated but not finitely presented submonoid of a free monoid.

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Vasily Ionin, Roman Mikhailov. 2026-08-20. The Parafree Conjecture for associative algebras. https://arxiv.org/abs/2608.20570

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