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We study etale topology and the notion of Azumaya algebra over a commutative ring constructively. As an application of the syntactic version of Barr's Theorem, we show the equivalence between two definitions of Azumaya algebra.
Externí odkaz:
http://arxiv.org/abs/2306.17679
Autor:
Simmons, William, Towsner, Henry
Publikováno v:
Pacific J. Math. 306 (2020) 721-754
Suppose $I$ is an ideal of a polynomial ring over a field, $I\subseteq k[x_1,\ldots,x_n]$, and whenever $fg\in I$ with degree $\leq b$, then either $f\in I$ or $g\in I$. When $b$ is sufficiently large, it follows that $I$ is prime. Schmidt-G\"ottsch
Externí odkaz:
http://arxiv.org/abs/1808.04805
Autor:
William Simmons, Henry Towsner
Publikováno v:
Pacific Journal of Mathematics. 306:721-754
Suppose $I$ is an ideal of a polynomial ring over a field, $I\subseteq k[x_1,\ldots,x_n]$, and whenever $fg\in I$ with degree $\leq b$, then either $f\in I$ or $g\in I$. When $b$ is sufficiently large, it follows that $I$ is prime. Schmidt-G\"ottsch