Morita Equivalence of Semigroups with Local Units
نویسنده
چکیده
We prove that two semigroups with local units are Morita equivalent if and only if they have a joint enlargement. This approach to Morita theory provides a natural framework for understanding McAlister’s theory of the local structure of regular semigroups. In particular, we prove that a semigroup with local units is Morita equivalent to an inverse semigroup precisely when it is a regular locally inverse semigroup.
منابع مشابه
Strong Morita equivalence for semigroups with local units
Morita equivalence is a widely used tool for rings with identity. (Two rings are said to be Morita equivalent if the categories of unitary modules over them are equivalent.) For monoids, this notion is not really useful: in most cases it reduces to isomorphism. As the theory of Morita equivalence could be developed for the more general case of rings with local units, and then for idempotent rin...
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