5 papers
Primes between 8th powers?
Matt Visser
OpenAI (using a non-public "internal frontier model'') has recently (6 October 2026) made a number of remarkable claims, including some claims regarding the quasi-Riemann hypothesi…
The finitistic weak dimensions of Gaussian rings
Xiaolei Zhang
We prove that every commutative Gaussian ring has finitistic weak dimension at most two. The proof works with a fixed module of finite flat dimension and does not assume that the w…
Module-Theoretic Characterizations of Prufer -Multiplication Domains
Xiaolei Zhang, Hwankoo Kim
We present unified -theoretic characterizations of Prüfer -multiplication domains (PMDs). A module-theoretic perspective shows that torsion submodules are -pure, and fo…
On generalized fraction and power series properties of -Noetherian rings
Xiaolei Zhang
In this note, we study the generalized fraction properties and power series properties of -Noetherian rings. Actually, we investigate two questions proposed in [A. Dab…
A note on a Cohen-type theorem for -Artinian modules
Xiaolei Zhang
In this note, we prove that a -module is -Artinian if and only if it is -cofinitely generated and for every prime -ideal of with $(0:_RM)\subsete…