A construction for absolute values in polynomial rings
A construction for absolute values in polynomial rings
复制标题
多项式环中绝对值的构造
DOI：
10.1090/s0002-9947-1936-1501879-8
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发表时间：
1936
影响因子：
1.3
通讯作者：
S. Maclane
中科院分区：
文献类型：
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作者：
S. Maclane
||B + c|| < max（||B||, ||C||）则值l| B||被称为非阿基米德（奥斯特洛夫斯基[17]，第272页）。这样定界的非阿基米德值具有相当大的算术意义。它们在整除性和不可约性的问题中很有用，事实上常常恰好对应于给定环的素理想。本文主要研究非阿基米德值的显式构造。更具体地说，给定有理数域R的所有这样的值，我们构造了系数在R中的x中的所有多项式的环R [x]的所有可能值。在处理非阿基米德值时，||一||通过相关的“指数”值
||b + c|| < max (||b||, ||c||) then the value l|b|| is called non-archimedean (Ostrowski [17], p. 272). The thus delimited non-archimedean values are of considerable arithmetic interest. They are useful in questions of divisibility and irreducibility and in fact often correspond exactly to the prime ideals of the given ring. This paper is devoted to the explicit construction of non-archimedean values. More specifically, given all such values for the field R of rational numbers, we construct all possible values of the ring R [x] of all polynomials in x with coefficients in R. In treating a non-archimedean value it is convenient to replace ||a|| by a related "exponential" value