A Short Proof for the Krull Dimension of a Polynomial Ring
نویسندگان
چکیده
منابع مشابه
A Short Proof for the Krull Dimension of a Polynomial Ring
A first important result in dimension theory is the fact that the Krull dimension of the ring K[X1, . . . , X`] is equal to ` when K is a field. In the literature this result is always obtained after some preliminary efforts that seem excessive for settling such an intuitive fact. For example, many authors rely on the principal ideal theorem of Krull, whose proof is very tricky. Matsumura [6,ch...
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A SHORT PROOF OF A RESULT OF NAGEL
Let $(R,fm)$ be a Gorenstein local ring and$M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are inthe same even liaison class, thenone has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2005
ISSN: 0002-9890
DOI: 10.2307/30037606