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Polynomial and Matrix Near-Rings

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Abstract

It is shown that, as for rings, a polynomial near-ring is a centralizer subnear-ring of an infinite matrix near-ring.

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References

  1. Bagley, S.: Polynomial near-rings, distributor ideals and J 2 ideals of generalized centralizer near-rings. Doctoral dissertation, Texas A&M University (1993)

  2. Bagley S.: Polynomial near-rings: polynomials with coefficients from a near-ring. In: Saad, G., Thomsen, (M. (eds) Nearrings, Nearfields and Loops., pp. 179–190. Kluwer, The Netherlands (1997)

    Chapter  Google Scholar 

  3. Clay J.R.: Nearrings: Geneses and Applications. Oxford Science Publications, New York (1992)

    MATH  Google Scholar 

  4. Farag, M.: On the structure of polynomial near-rings. Doctoral dissertation, Texas A&M University (1999)

  5. Farag M.: A new generalization of the center of a near-ring with applications to polynomial near-rings. Comm. Algebra 29, 2377–2387 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lausch H., Nöbauer W.: Algebra of Polynomials. North Holland, Amsterdam (1973)

    MATH  Google Scholar 

  7. Lee E.K.S.: Theory of polynomial near-rings. Comm. Algebra 32, 1619–1635 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lee E.K.S., Groenewald N.J.: Polynomial near-rings in k indeterminates. Bull. Austral. Math. Soc. 70, 441–449 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. le Riche L.R., Meldrum J.D.P., van der Walt A.P.J.: On group near-rings. Arch. Math. 52, 132–139 (1989)

    Article  Google Scholar 

  10. Meldrum J.D.P., van der Walt A.P.J.: Matrix near-rings. Arch. Math. 47, 312–319 (1986)

    Article  MATH  Google Scholar 

  11. Meyer, J.H.: Matrix near-rings. Ph.D. thesis, University of Stellenbosch (1986)

  12. Pilz G.: Near-Rings. North Holland, Amsterdam (1983)

    MATH  Google Scholar 

  13. Veldsman S.: Homomorphic images of polynomial near-rings. Contr. Algebra Geometry 50, 119–142 (2009)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Stefan Veldsman.

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Veldsman, S. Polynomial and Matrix Near-Rings. Arab J Sci Eng 36, 1039–1046 (2011). https://doi.org/10.1007/s13369-011-0089-x

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  • DOI: https://doi.org/10.1007/s13369-011-0089-x

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