| 释义 |
ˈsemi-group Math.
[ad. F. semi-groupe (J.-A. de Séguier Élem. de la Théorie des Groupes Abstraits (1904), i. 8); cf. semi- 8.]
A set together with an associative binary operation under which it is closed.
1904Bull. Amer. Math. Soc. XI. 160 The author [sc. de Séguier] introduces..a semigroup G in connection with any subset S containing a system of generators of G. The postulates defining G are: (1) associativity; (2) for any a in S and b in G, there is at most one solution (n in G) of an = b; (3) similarity for na = b. 1905Trans. Amer. Math. Soc. VI. 205 The correct theorem involves the concept semi-group, which reduces to a group when there is a finite number of elements, but not in general for an infinitude of elements. 1968P. A. P. Moran Introd. Probability Theory ii. 66 The convolution operation..has some of the properties of multiplication in that it is associative..and commutative,..but division is not in general possible. With this operation the set of all discrete distributions on (0, 1,{ddd}) is therefore said to form a ‘semi-group’. 1972A. G. Howson Handbk. Terms Algebra & Anal. v. 25 A semigroup..possessing..an identity element..is called a monoid. 1979Proc. London Math. Soc. XXXVIII. 335 First we find exactly when the resolvent operators and the semigroup operators are strong Feller operators. |