At present I see only one paper by John Meldrum and M. Samman: On endomorphisms of semilattices of groups (=Clifford semigroups) from 2005 in Algebra Colloquium 12, 93-100. A further paper is announced, but I cannot find it.
For the generalized case of a partial module(strong semilattice of modules) over a partial ring (strong semilattices of rings) , see Lemma 3.2 in the paper "Generalized Modules over Semilattices of Rings" by M.El-Ghali M.Abdallah.
Dear M.El-Ghali Mohamed Abdallah,
Can you send me this paper? Thank you.
Dear Ahmed Munir, this is true, but for which Clifford semigroups do all homomorphisms between the subgroups come from endomorphisms of the Clifford semigroup?
Dear Ulrich Knauer, A pdf of that paper is allowed in my home page on Research Gate.About your question,it is not that easy to extend a homomorphism between two maximal groups in a Clifford semigroup(semilattice of groups) to the Clifford semigroup except under certain conditions on the connecting mappings.Actually the problem is that,if wee have a collection of homomorphisms between the maximal groups in a Clifford semigroup indexed by its semilattice of idempotents ,how can this colliction be extended to a single endomorphism of the Clifford semigroup?
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