Takanori Nagamine

activity

20182026

collaborators

10 papers

math.AC2026

Quasi-factorially closed subalgebras of Laurent polynomial rings

Shinya Kumashiro, Takanori Nagamine

Let $R$ be a domain and $B = R [x_{1}^{\pm 1}, \dots, x_{n}^{\pm 1}]$ the Laurent polynomial ring over $R$ . In this paper we study pre-factorially closed (pfc) and quasi-factorially closed (…

math.AC2024

Remarks on retracts of polynomial rings in three variables in any characteristic

Hideo Kojima, Takanori Nagamine, Riko Sasagawa

Let $A$ be a retract of the polynomial ring in three variables over a field $k$ . It is known that if $char (k) = 0$ or $tr.deg_{k} A \neq = 2$ then $A$ is a polynomial…

math.AG2023

Affine and Unirational unique factorial domains with unmixed gradings

Gene Freudenburg, Takanori Nagamine

This paper studies the class of unique factorial domains $B$ over an algebraically closed field $k$ which are affine or unirational over $k$ and which admit an effective unmixed $\…

math.AC2023

Retracts of Laurent polynomial rings

Neena Gupta, Takanori Nagamine

Let $R$ be an integral domain and $B = R [x_{1}, \dots, x_{n}]$ be the polynomial ring. In this paper, we consider retracts of $B [1/ M]$ for a monomial $M$ . We show that (1) if $M=\prod_{i=…

math.AC2021

Generalizations of Samuel's criteria for a ring to be a unique factorization domain

Daniel Daigle, Gene Freudenburg, Takanori Nagamine

We give several criteria for a ring to be a UFD including generalizations of some criteria due to P. Samuel. These criteria are applied to construct, for any field k, (1) a Z-grade…

math.AG2019

Smooth factorial affine surfaces of logarithmic Kodaira dimension zero with trivial units

Gene Freudenburg, Hideo Kojima, Takanori Nagamine

This paper considers the family $S_{0}$ of smooth affine factorial surfaces of logarithmic Kodaira dimension 0 with trivial units over an algebraically closed field $k$ . Ou…