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On uniform acts over semigroups

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Abstract

The paper is devoted to the investigation of uniform acts over semigroups perceived as an overclass of subdirectly irreducible acts. We establish conditions for a uniform act to be subdirectly irreducible. In particular, we prove that uniform acts with two zeros are subdirectly irreducible. Ultimately we investigate monoids which are uniform as right acts over themselves and we describe regular monoids with this property.

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References

  1. Berthiaume, P.: The injective envelope of \(S\)-sets. Canad. Math. Bull. 10(2), 261–272 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  2. Feller, E.H., Gantos, R.L.: Indecomposable and injective \(S\)-systems with zero. Math. Nachr. 41(1), 37–48 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  3. Goldie, A.W.: The structure of prime rings under ascending chain conditions. Proc. Lond. Math. Soc. 8(3), 589–608 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  4. Goldie, A.W.: Semi-prime rings with maximum condition. Proc. Lond. Math. Soc. 10(3), 201–220 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kilp, M., Knauer, U., Mikhalev, A.V.: Monoids, Acts and Categories, With Application to Wreath Product. Walter de Gruyter, Berlin (2000)

  6. Kozhukhov, I.B.: One characteristical property of semilattices. Commun. Algebra. 25, 2569–2577 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kozhukhov, I.B.: Finiteness conditions for subdirectly irreducible acts and modules. Fundam. Appl. Math. 4, 1–5 (1998). (in Russian)

    MathSciNet  MATH  Google Scholar 

  8. Kozhukhov, I.B.: Semigroups over which all acts are residually finite. Fund. Appl. Math. 4, 1335–1344 (1998). (in Russian)

    MathSciNet  MATH  Google Scholar 

  9. Kozhukhov, I.B., Haliullina, A.R.: A characterization of subdirectly irreducible acts. Prikl. Diskretn. Mat. (27), 5–16 (2015). (in Russian)

  10. Rankin, S.A., Reis, C.M., Thierrin, G.: Right subdirectly irreducible semigroups. Pac. J. Math. 85(2), 403–412 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  11. Renshaw, J.: Monoids for which condition (P) acts are projective. Semigroup Forum 61, 46–56 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sedaghatjoo, M., Naghipoor, M.A.: An approach to injective acts over monoids based on indecomposability. Commun. Algebra 45(7), 3005–3016 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang, X., Knauer, U., Chen, Y.: Classification of monoids by injectivities I. C-injectivity. Semigroup Forum 76, 169–176 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We have to express our appreciation to an anonymous referee for the careful reading of the manuscript and for enhancing its contents.

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Authors and Affiliations

  1. College of Engineering, Lamerd Higher Education Center, Lamerd, Iran

    Mohammad Roueentan

  2. Department of Mathematics, College of Sciences, Persian Gulf University, Bushehr, Iran

    Mojtaba Sedaghatjoo

Authors
  1. Mohammad Roueentan
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  2. Mojtaba Sedaghatjoo
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Correspondence to Mojtaba Sedaghatjoo.

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Communicated by László Márki.

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Roueentan, M., Sedaghatjoo, M. On uniform acts over semigroups. Semigroup Forum 97, 229–243 (2018). https://doi.org/10.1007/s00233-017-9908-z

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  • DOI: https://doi.org/10.1007/s00233-017-9908-z

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