Sardar, Sujit Kumar; Gupta, Sugato A note on Morita invariants of semigroups. (English) Zbl 1344.20081 Semigroup Forum 92, No. 1, 71-76 (2016). 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. Cited in 3 Documents 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 Keywords:Morita invariants; semigroups with weak local units; Morita contexts; lattice isomorphisms; strong Morita equivalences of semigroups; bi-acts PDFBibTeX XMLCite \textit{S. K. Sardar} and \textit{S. Gupta}, Semigroup Forum 92, No. 1, 71--76 (2016; Zbl 1344.20081) Full Text: DOI References: [1] Anjaneyulu, A.: Primary ideals in semigroups. Semigroup Forum 20, 129-144 (1980) · Zbl 0441.20041 [2] Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups, vol. II. American Mathematical Society, Providence (1967) · Zbl 0178.01203 [3] Laan, V., Márki, L.: Morita invariants for semigroups with local units. Monatsh. Math. 166, 441-451 (2012) · Zbl 1256.20054 [4] Lam, T.Y.: Lectures on Modules and Rings. Springer-Verlag, New York (1999) · Zbl 0911.16001 [5] Luh, J.: On the concepts of radical of semigroup having kernel. Port. Math. 19, 189-198 (1960) · Zbl 0095.01405 [6] Ouyang, B.Y., Tong, W.T.: Morita context and Morita-like equivalence for the xst-rings. Acta Math. Sin. (English series) 19, 371-380 (2003) · Zbl 1025.16006 [7] Steinfeld, O.: Quasi-ideals in Rings and Semigroups. Akadémiai Kiadó, Budapest (1978) · Zbl 0403.16001 [8] Targla, T., Laan, V.: Congruences of stongly Morita equivalent posemigroups. Acta Math. Univ. Comen. 81, 247-254 (2012) · Zbl 1274.06056 [9] Tart, L.: Morita invariants for partially ordered semigroups with local units. Proc. Est. Acad. Sci. 61, 38-47 (2012) · Zbl 1263.06006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.