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Abstract
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This paper addresses conditions under which all generators in the category
of right S-acts (where S is a monoid) satisfy a flatness property. There are characterizations for monoids over which all generators satisfy a flatness property ? where ? can stand for freeness, projectivity, strong flatness, Condition (P), principal weak flatness and torsion freeness. To our knowledge, the problem has not been studied for other flatness properties such as weak flatness, Condition (E) and regularity. The present paper addresses this gap.
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