Afrika Matematika

, Volume 29, Issue 3–4, pp 371–381 | Cite as

Gabriel topology related to Morita context of semirings

Article
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Abstract

In this paper we introduce the notion of Gabriel topology on semirings as well as on bisemimodules with unities. We also show that there is a lattice isomorphism between the Gabriel topologies on semirings and those on bisemimodules connected via Morita context.

Keywords

Pretopology Gabriel topplogy Essential ideal Morita equivalence Morita context 

Mathematics Subject Classification

16D90 16Y60 

References

  1. 1.
    Dutta, T.K., Dhara, S.: On uniformly strongly prime \(\Gamma \)-semirings-II. Gen. Algebra Appl. 26, 219–231 (2006)MathSciNetMATHGoogle Scholar
  2. 2.
    Dutta, T.K., Das, M.L.: Normal radical class of semirings. Southeast Asian Bull. Math. 35(3), 389–400 (2011)MathSciNetMATHGoogle Scholar
  3. 3.
    Dutta, T.K., Sardar, S.K.: On the operator semirings of a \(\Gamma \)-semiring. Southeast Asian Bull. Math. 26, 203–213 (2002)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Golan, J.S.: Semirings and Their Applications. Kluwer Academic Publishers, Dordrecht (1999)CrossRefMATHGoogle Scholar
  5. 5.
    Katsov, Y.: Tensor products and injective envelopes of semimodules over additively regular semirings. Algebra Colloq. 4(2), 121–131 (1997)MathSciNetMATHGoogle Scholar
  6. 6.
    Katsov, Y., Nam, T.G.: Morita equivalence and homological characterization of semirings. J. Algebra Appl. 10(3), 445–473 (2011)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Mac Lane, S.: Categories for Working Mathematician, 2nd edn. Springer-Verlag Inc., New York (1998)MATHGoogle Scholar
  8. 8.
    Sardar, S.K., Gupta, S., Saha, B.C.: Morita equivalence of semirings and its connection with Nobusawa \(\Gamma \)-semirings with unities. Algebra Colloq. 22(spec01), 985–1000 (2015)Google Scholar
  9. 9.
    Sardar, S.K., Gupta, S.: Morita invariants of semirings. J. Algebra Appl. 15, 1650023 (2016)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Stenstorm, B.: Rings of Quotients. Springer, Berlin (1975)CrossRefGoogle Scholar
  11. 11.
    Vandiver, H.S.: Note on a simple type of algebra in which the cancellation law of addition does not hold. Bull. Am. Math. Soc. 40, 914–920 (1934)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  • Sujit Kumar Sardar
    • 1
  • Krishanu Dey
    • 1
  • Sugato Gupta
    • 1
  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia

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