Enlargements and Morita contexts for semirings

In this paper, we study enlargements and Morita contexts for factorizable semirings. These are semirings, where each element is a finite sum of products of some elements. We show that a full matrix semiring over a factorizable semiring is an enlargement of that semiring. We call two factorizable semirings Morita equivalent if they are connected by a unitary and surjective Morita context. It turns out that two factorizable semirings are Morita equivalent if and only if they have a joint enlargement. We prove that each unitary Morita context between factorizable semirings is isomorphic to a Morita context that is induced by a joint enlargement of those semirings. Finally, we study Morita invariants for semirings. Differently from the case of rings or semigroups, regularity is not a Morita invariant for semirings with identity. We prove that if two commutative factorizable nondegenerate semirings are Morita equivalent, then they are isomorphic.