• LEFT I-ORDERS IN STRONG SEMILATTICES OF PROPER BISIMPLE INVERSE SEMIGROUPS

N. GHRODA*

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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