13 papers
A one-dimensional coherent domain with non-Prüfer integral closure
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
In a question recorded in 1978, Vasconcelos asked whether the integral closure of a one-dimensional coherent local domain in its fraction field is Prüfer. We construct such a domai…
Dimensions of a ring and its formal power series ring
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
Understanding the relation between and is a classical problem in commutative algebra. For a Noetherian ring , one has , but the gene…
Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
We prove Bouvier's conjecture. More generally, an integer sequence with is realized by a unique factorization domain (UFD) with $\dim R[X_1,\ldo…
The Erdős-Hajnal Property for the six-vertex Graph with Edge Set
Viet-Hoang Tran, Tan M. Nguyen
We prove that the six-vertex graph with edge set has the Erdős-Hajnal property. The proof adapts the iterative-sparsification method of Nguyen, Scott, an…
Polynomial extensions do not preserve the strong finite type property
Viet-Hoang Tran, Phan Thanh Toan, Thieu N. Vo +1
Arnold introduced the strong finite type (SFT) property in 1973 while studying the dimension of power series rings. For several classes of rings, polynomial extension is known to p…
The Noetherian Case of Bayart's Power-Series Question
Viet-Hoang Tran, Dung V. Nguyen, Quang X. Nguyen +2
Let be a commutative Noetherian ring. We prove that if the one-variable formal power-series ring is a unique factorization domain, then so is the two-variable formal p…