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E-free objects inE-varieties of inverse rings

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Abstract

We show that for any regular ring (R, +, -), the following conditions are equivalent:

  1. (i)

    (R, -) is inverse.

  2. (ii)

    (R, -) isE-solid.

  3. (iii)

    (R, -) is locally inverse.

  4. (iv)

    (R, -) is locallyE-solid.

We also show that there is ane-free object in eache-variety of inverse rings.

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References

  1. Clifford, A.H. and G.B. Preston, “The Algebraic Theory of Semigroups,” Vol. I, Math. Surveys Amer. Math. Soc.7, Providence, R.I., 1961.

  2. Burris, S. and H.P. Sankappanavar, “A course in Universal Algebra,” Graduate Texts in Mathematics78, Springer-Verlag, New York, Heidelberg, Berlin, 1981.

    Google Scholar 

  3. Grätzer, G. “Universal Algebra,” Van Nostrand, New York, 1968.

    MATH  Google Scholar 

  4. Hall, T.E.On regular semigroups, J. Algebra24 (1973), 1–24.

    Article  MATH  MathSciNet  Google Scholar 

  5. Hall, T.E.Identities for existence varieties of regular semigroups, Bull. Austral. Math. Soc.40 (1989), 59–77.

    MATH  MathSciNet  Google Scholar 

  6. Yeh, Y.T.The existence of e-free objects in e-varieties of regular semigroups, International Journal of Algebra and Computation2 No. 4 (1992), 471–484.

    Article  MATH  MathSciNet  Google Scholar 

  7. Zeleznikow, J.,Orthodox semirings and rings, J. Austral. Math. Soc. Series A30 (1980), 50–54.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Monash University, 3168, Clayton, Victoria, Australia

    Jean Oesmer Loyola

Authors
  1. Jean Oesmer Loyola
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Communicated by T.E. Hall

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Loyola, J.O. E-free objects inE-varieties of inverse rings. Semigroup Forum 54, 375–380 (1997). https://doi.org/10.1007/BF02676618

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  • DOI: https://doi.org/10.1007/BF02676618

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