The S-act theory for semigroups is recognized as an important theory in studying semigroups from the external action,and flat S-acts are important research objects in this theory.A general form of flat acts called GP-flat acts is introduced.By exploring the relationship between GP-flat acts and direct products(coproducts,torsion free acts),some basic properties of GP-flat acts are given.By investigating GP-flatness of acts,semigroups with local units are are characterized.Furthermore,many known results are generalized.This research will further apply the S-acts theory to semigroups.Meanwhile,it will have an important significance in revealing the differences and connections between semigroup theory and monoid theory,and exploring the application of flat acts in semigroup theory.
semigroups with local unitsgenerally regular semigroupsS-actsprincipally weakly flat actsGP-flat acts
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