• LEFT I-ORDERS IN STRONG SEMILATTICES OF PROPER BISIMPLE INVERSE SEMIGROUPS
Abstract
Let be an inverse semigroup. A subsemigroup of is a left I-order in and is a semigroup of left I-quotients of if every element can be written as for some . We characterize semigroups which are left I-quotients of semigroups which are strong semilattices of right cancellative monoids with the (LC) condition and certain further conditions. We give necessary and sufficient conditions for to be proper.
Keywords
I-orders, I-quotients, right cancellative monoid, inverse hull.
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