ALMOST INJECTIVE TRANSFORMATIONS OF AN INFINITE SET

作者：Mendes Goncalves Suzana^*; Sullivan R P

来源：Communications in Algebra, 2012, 40(1): 192-205.

DOI：10.1080/00927872.2010.527880

• Almost one-to-one transformations
• Green%26apos
• s relations
• Ideals

Let V be an infinite-dimensional vector space, let n be a cardinal such that N-0 %26lt;= n %26lt;= dim V, and let AM(V, n) denote the semigroup consisting of all linear transformations of V whose nullity is less than n. In recent work, Mendes-Goncalves and Sullivan studied the ideal structure of AM(V, n). Here, we do the same for a similarly-defined semigroup AM(X, q) of transformations defined on an infinite set X. Although our results are clearly comparable with those already obtained for AM(V, n), we show that the two semigroups are never isomorphic.

• 出版日期2012