Author

Xiao-Jin Zhang

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Preprint Sep 2026

Igusa--Todorov Algebras and the Auslander--Reiten Conjecture

We prove that every Igusa--Todorov Artin algebra satisfies the Auslander--Reiten conjecture. More precisely, let $V$ be an $n$-Igusa--Todorov witness, and let $t$ be the number of isomorphism classes of nonprojective indecomposable summands of $V$. If a finitely generated module $M$ satisfies $\Ext_A^i(M,A)=0$ for ever...

Xiao-Jin Zhang, Pan-Yue Zhou · 0 citations

Preprint Sep 2026

The Auslander-Reiten conjecture for algebras with radical cube zero

Let $A$ be a split finite-dimensional algebra over a field whose radical $J$ satisfies $J^3=0$, and let $s$ be the number of isomorphism classes of simple $A$-modules. We prove that a non-projective module $M$ with ${\rm Ext}_A^i(M,A)=0$ for all $i>0$ has a non-zero self-extension in some degree between $1$ and $3s+1$....

Xiao-Jin Zhang, Pan-Yue Zhou · 0 citations