The Free AMPLE Monoid
نویسندگان
چکیده
We show that the free weakly E-ample monoid on a set X is a full submonoid of the free inverse monoid FIM(X) on X . Consequently, it is ample, and so coincides with both the free weakly ample and the free ample monoid FAM(X) on X . We introduce the notion of a semidirect product Y ∗ T of a monoid T acting doubly on a semilattice Y with identity. We argue that the free monoid X∗ acts doubly on the semilattice Y of idempotents of FIM(X) and that FAM(X) is embedded in Y ∗ X∗. Finally we show that every weakly E-ample monoid has a proper ample cover.
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ورودعنوان ژورنال:
- IJAC
دوره 19 شماره
صفحات -
تاریخ انتشار 2009