Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Nagamine, Takanori"'
Let $A$ be a retract of the polynomial ring in three variables over a field $k$. It is known that if ${\rm char}\: (k) = 0$ or ${\rm tr.deg}\:_k A \not= 2$ then $A$ is a polynomial ring. In this paper, we give some sufficient conditions for $A$ to be
Externí odkaz:
http://arxiv.org/abs/2412.13424
Autor:
Freudenburg, Gene, Nagamine, Takanori
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 $\mathbb{Z}^{d-1}$-grading with $B_0=k$, where $d$ is the dimension of $
Externí odkaz:
http://arxiv.org/abs/2307.05859
Autor:
Nagamine, Takanori
Let $R$ be an integral domain and $B=R[x_1,\ldots,x_n]$ be the polynomial ring. In this paper, we consider retracts of $B[1/M]$ for a monomial $M$. We show that (1) if $M=\prod_{i=1}^nx_i$, then every retract is a Laurent polynomial ring over $R$, (2
Externí odkaz:
http://arxiv.org/abs/2301.12681
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-graded non-noetherian rational UFD of dimension three over k, and (2) k-aff
Externí odkaz:
http://arxiv.org/abs/2102.06642
This paper considers the family $\mathscr{S}_0$ of smooth affine factorial surfaces of logarithmic Kodaira dimension 0 with trivial units over an algebraically closed field $k$. Our main result (Theorem 4.1) is that the number of isomorphism classes
Externí odkaz:
http://arxiv.org/abs/1910.03494
Autor:
Nagamine, Takanori
In this paper, we study higher derivations of Jacobian type in positive characteristic. We give a necessary and sufficient condition for $(n-1)$-tuples of polynomials to be extendable in the polynomial ring in $n$ variables over an integral domain $R
Externí odkaz:
http://arxiv.org/abs/1905.10068
Autor:
Freudenburg, Gene, Nagamine, Takanori
Over a field $k$, we study rational UFDs of finite transcendence degree $n$ over $k$. We classify such UFDs $B$ when $n=2$, $k$ is algebraically closed, and $B$ admits a positive $\mathbb{Z}$-grading, showing in particular that $B$ is affine over $k$
Externí odkaz:
http://arxiv.org/abs/1812.04979
Autor:
Nagamine, Takanori
Publikováno v:
Journal of Algebra, Volume 534, 15 September 2019, Pages 339-343
In Costa's paper published in 1977, he asks us whether every retract of $k^{[n]}$ is also the polynomial ring or not, where $k$ is a field. In this paper, we give an affirmative answer in the case where $k$ is a field of characteristic zero and $n =
Externí odkaz:
http://arxiv.org/abs/1811.04153
Publikováno v:
In Journal of Algebra 15 March 2022 594:271-306
