| 释义 |
nilpotent, a. Math.|nɪlˈpəʊtənt|
[f. nil2 + L. potent-, potens powerful, potent a.1]
Becoming zero when raised to some positive integral power (see also quot. 1949).
1870B. Peirce in Amer. Jrnl. Math. (1881) IV. 104 When an expression raised to the square or any higher power vanishes, it may be called nilpotent. 1937A. A. Albert Mod. Higher Algebra (1938) iv. 87 Two nilpotent matrices of index two are similar in F if and only if they have the same rank. 1949S. Kravetz tr. Zassenhaus's Theory of Groups iv. 111 A group G is said to be nilpotent if the ascending central series contains the whole group as a member. 1971I. T. Adamson Rings, Modules & Algebras xxiii. 194 We say that I is a nilpotent ideal if there exists a positive integer n such that In is the zero ideal. 1974T. W. Hungerford Algebra vii. 100 We obtain a sequence of normal subgroups of G, called the ascending central series of G: 〈e〉 1(G) 2(G) n(G) = G for some n. Ibid. 102 A group G is said to be solvable if G(n) = 〈e〉 for some n... Every nilpotent group is solvable. |