On the existence of a regular factorial subring and a p-basis of a polynomial ring in two variables in characteristic p=3

Tomoaki Ono

doi:10.55937/sut/1415457453

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Home > Journals > SUT J. Math. > Volume 50 > Issue 1 > Article

January 2014 On the existence of a regular factorial subring and a

p

-basis of a polynomial ring in two variables in characteristic

p = 3

Tomoaki Ono

Author Affiliations +

Tomoaki Ono¹
¹Tokyo Metropolitan College of Industrial Technology 8-52-1, Minami-senju, Arakawa-ku, Tokyo 116-8523, Japan

SUT J. Math. 50(1): 1-17 (January 2014). DOI: 10.55937/sut/1415457453

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Abstract

When $K$ is an algebraically closed field of characteristic $p{\rm{\;}} = {\rm{\;}}3$ , we shall investigate the existence of a regular factorial subring $R^{'}$ of $R{\rm{\;}} = {\rm{\;}}K[x,{\rm{\;}}y]$ containing ${R^p} = K[{x^p},\,{y^p}]$ and the existence of a $p$ -basis of $R$ over $R^{'}$ .

Acknowledgment

The author would like to express his/her hearty thanks to the referee for many useful suggestions that improved this paper. In particular, Lemma 3.3 is suggested by the referee.

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Tomoaki Ono. "On the existence of a regular factorial subring and a $p$ -basis of a polynomial ring in two variables in characteristic $p = 3$ ." SUT J. Math. 50 (1) 1 - 17, January 2014. https://doi.org/10.55937/sut/1415457453