| 释义 |
▪ I. Aˈbelian, ˈAbelite, Abeˈlonian Eccl. Hist.
[f. Abel, Gen. iv. 8.]
A member of a small sect of ancient heretics in the north of Africa, stated by Augustine to have lived in continence after marriage, after the alleged example of ‘the righteous Abel.’
1751Chambers Cyc. s.v. Who in this footing should have been called Adamites rather than Abelians.
▪ II. Abelian, a. Math.|əˈbiːlɪən|
Also abelian.
[f. the name of Niels Henrik Abel (1802–29), Norwegian mathematician + -ian.]
Of, pertaining to, or designating certain mathematical concepts to which Abel's research contributed; spec. (a) an integral of a function of two variables which are related to one another by an algebraic equation; (b) an equation all of whose roots are rational functions of one of them; (c) [after F. groupe abélien (C. Jordan Traité des Substitutions (1870) ii. ii. 172)], a group whose binary operation is commutative.
1847Rep. Brit. Assoc. Adv. Sci. 1846 i. 75 What are the corresponding functions to which the hyper-elliptic or Abelian integrals are inverse, and how by means of them can Abel's theorem be stated? 1861Ibid. 1860 i. 126 This equation is of the kind called Abelian; that is to say, each of the e periods is a rational function of any other. 1897[see integrand]. 1898Q. Jrnl. Math. XXIX. 169 This paper generalizes to the Galois Field the work of Jordan..on the decomposition of the Abelian group, studied earlier by Hermite in connection with the transformation of Abelian functions. 1972M. Kline Math. Thought xxvii. 655 Work on the inversion of hyperelliptic and Abelian integrals up to the entry of Riemann on the scene was hampered by the limited methods of handling multiple-valued functions. Ibid. xxxi. 755 The cyclotomic equation..is an example of an Abelian equation. 1976Sci. Amer. Nov. 55/1 Maxwell's theory is an Abelian gauge theory; non-Abelian gauge theories are distinguished from it by the fact that the fields themselves carry quantum numbers. 1982W. S. Hatcher Logical Found. Math. viii. 241 Other examples of systems we will wish to call categories are the following..the class of abelian groups as objects with group homomorphisms as mappings. |