全变换半群的极大半传递幺半群(英文)

Maximal Half-transitive Submonoids of Full Transformation Semigroups

对任一个非空集X,X上的全变换半群T(X)的一个子幺半群M被称为半传递,如果M为非传递,且对每个序对(x,y)∈X×X,存在∈M使x=y或y=x.本文刻画了全变换半群T(X)的所有极大半传递子幺半群;对T(X)的每个极大半传递子幺半群M,相关秩r(T(X),M)被证明为1.对有限集X,给出T(X)的极大半传递子幺半群的个数,且T(X)的最大基数的半传递子幺半群被刻画.

For an arbitrary non-empty set X, a submonoid M of the semigroup T（X） of full transformations on X is said to be half-transitive provided that it is intransitive, and for every ordered pair （x,y） ∈ X ×X there is some φ∈M such that either xφ = y or yφ = x. In this paper all maximal half-transitive submonoids of T（X） ave described. The relative rank r（T（X）, M） is shown to be 1 for every maximal half-transitive submonoid M of T（X）. For a finite set X, the number of maximal half-transitive submonoids of T（X） is counted, and the largest half-transitive submonoids of T（X） are described.