Author

Xin Zhang

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Preprint Sep 2026

An explicit rational lemniscate counterexample with certified separators

In the setting of the previously reported degree-seven counterexample of ani, we present an explicit monic polynomial with real rational coefficients and a direct proof by certified separators. The polynomial has seven simple zeros in the open unit disk. Every continuous path joining distinct zeros in its closed unit s...

Jiang Yang, Xin Zhang · 0 citations

Preprint Sep 2026

Singular Submodules of Abelian Groups over Their Endomorphism Rings

Let $A$ be an abelian group and $E=\Endo_{\Z}(A)$. We give a module-theoretic description of the singular $E$-submodules asked for in Fuchs'Problem~1.2. For a unital ring $R$ and a left $R$-module $M$, put $W=I_R({}_RR)\oplus I_R(M)$ and $J=\Jaco(\Endo_R(W))$, and let $u$ be the image of $1_R$. The classical essential-...

Jiang Yang, Xin Zhang · 0 citations