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A note on Morita invariants of semigroups. (English) Zbl 1344.20081

Summary: In this paper we observe that important ideals like prime ideals, nil ideals, nilpotent ideals, primary ideals etc. remain invariant under strong Morita equivalence of semigroups with weak local units. As a consequence, some radicals and important properties are found to be invariant. Finally, lattice isomorphisms between the set of all ideals and the set of all sub-biacts corresponding to a Morita context of the said class of semigroups are established.

MSC:

20M50 Connections of semigroups with homological algebra and category theory
20M30 Representation of semigroups; actions of semigroups on sets
20M12 Ideal theory for semigroups
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