Krull dimension

If $R$ is a ring, the Krull dimension (or simply dimension) of $R$ , $\\dim R$ is the supremum of all integers $n$ such that there is an increasing sequence of prime ideals $\\mathfrak{p}_{0}\\subsetneq\\cdots\\subsetneq\\mathfrak{p}_{n}$ of length $n$ in $R$ .

If $X$ is a topological space, the Krull dimension (or simply dimension) of $X$ , $\\dim X$ is the supremum of all integers $n$ such that there is a decreasing sequence of irreducible closed subsets $F_{0}\\supsetneq\\cdots\\supsetneq F_{n}$ of $X$ .

单词	KrullDimension
释义	Krull dimension If $R$ is a ring, the Krull dimension (or simply dimension) of $R$ , $\\dim R$ is the supremum of all integers $n$ such that there is an increasing sequence of prime ideals $\\mathfrak{p}_{0}\\subsetneq\\cdots\\subsetneq\\mathfrak{p}_{n}$ of length $n$ in $R$ . If $X$ is a topological space, the Krull dimension (or simply dimension) of $X$ , $\\dim X$ is the supremum of all integers $n$ such that there is a decreasing sequence of irreducible closed subsets $F_{0}\\supsetneq\\cdots\\supsetneq F_{n}$ of $X$ .
随便看	monotone class MonotoneClassTheorem monotone class theorem MonotoneConvergenceTheorem monotone convergence theorem Monotonic monotonic MonotonicallyDecreasing monotonically decreasing MonotonicallyIncreasing monotonically increasing MonotonicallyNondecreasing monotonically nondecreasing MonotonicallyNonincreasing monotonically nonincreasing MonotonicityCriterion monotonicity criterion MonotonicityOfTheSequence1Xnn monotonicity of the sequence (1+x/n)^n MonteCarloMethods Monte Carlo methods MonteCarloSimulation Monte Carlo simulation MontelsTheorem Montel’s theorem