Rings Satisfying the Three Noether Axioms.

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI:10.32917/HMJ/1206138646

J. Gilbert, H. Butts

引用次数: 2

Abstract

This paper is concerned with the ideal theory of a commutative ring R (which may not have an identity). We say that R is integrally closed in its total quotient ring T (or, simply, integrally closed) provided R contains every element a e T such that a is integral over R (i, e., a + rιa~-\ [-rn = 0 for some ri, ..., rn in R). A ring R is n-dimensional (n a, non-negative integer), or has dimension n (dim R = n), provided there exists a chain P0

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满足三诺特公理的环。

本文讨论了交换环R(可能没有恒等环)的理想理论。我们说R在它的全商环T中是整闭的(或者，简单地说，是整闭的)，前提是R包含每个元素a e T，使得a对R (i, e, a + rii a~-\ [-rn = 0，对于某些ri，…一个环R是n维的(n A，非负整数)，或有n维(dim R = n)，只要存在R中的素理想链P0

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry

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