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A note on Morita invariants of semigroups

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Abstract

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.

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References

  1. Anjaneyulu, A.: Primary ideals in semigroups. Semigroup Forum 20, 129–144 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  2. Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups, vol. II. American Mathematical Society, Providence (1967)

    MATH  Google Scholar 

  3. Laan, V., Márki, L.: Morita invariants for semigroups with local units. Monatsh. Math. 166, 441–451 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lam, T.Y.: Lectures on Modules and Rings. Springer-Verlag, New York (1999)

    Book  MATH  Google Scholar 

  5. Luh, J.: On the concepts of radical of semigroup having kernel. Port. Math. 19, 189–198 (1960)

    MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  7. Steinfeld, O.: Quasi-ideals in Rings and Semigroups. Akadémiai Kiadó, Budapest (1978)

    MATH  Google Scholar 

  8. Targla, T., Laan, V.: Congruences of stongly Morita equivalent posemigroups. Acta Math. Univ. Comen. 81, 247–254 (2012)

    MathSciNet  Google Scholar 

  9. Tart, L.: Morita invariants for partially ordered semigroups with local units. Proc. Est. Acad. Sci. 61, 38–47 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

We are thankful to Prof. Valdis Laan and Prof. László Márki as well as to the learned referee for their meticulous review and subsequent valuable remarks, suggestions and necessary corrections in order to improve the paper in presentation and content. The second author is grateful to the University Grants Commission, Govt. of India, for providing research support as SRF.

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Correspondence to Sujit Kumar Sardar.

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Communicated by László Márki.

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Sardar, S.K., Gupta, S. A note on Morita invariants of semigroups. Semigroup Forum 92, 71–76 (2016). https://doi.org/10.1007/s00233-014-9682-0

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  • DOI: https://doi.org/10.1007/s00233-014-9682-0

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