Results in Mathematics

, Volume 29, Issue 1–2, pp 125–136 | Cite as

Boolean Orthogonalities For Near-rings



Cornish has developed a theory of Boolean orthogonalities for sets with an associated algebraic closure system of “ideals”, and applied it to reduced rings and semiprime rings. In this paper we apply the theory to near-rings and in particular to 3-somiprime near-rings. As one consequence, we identify some near-rings whose 3-semiprime ideals are intersections of 3-prime ideals. In the final section, we discuss local ideals and normality conditions for near-rings with a. Boolean orthogonality.


Prime Ideal Maximal Ideal Local Ideal Semiprime Ring Minimal Prime Ideal 
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  1. 1.
    G. Birkenmeier, H. Heatherly and E. Leo, Prime ideals in near-rings, Res. in Math. 24 (1993), 27–4K.MATHCrossRefGoogle Scholar
  2. 2.
    G. Booth and N. Groenewald, v-Prime and v-Semiprime Near-rings, submitted.Google Scholar
  3. 3.
    W. Cornish, Boolean orthogonalities and minimal prime ideals, Coinni. Algebra 3 (1975), 859–900.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    .J. Fisher and R. Snider, On the von Neumann regularity of rings with regular prime factor rings, Pacific J. Math. 54 (1974), 135–144.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    N. Groenewald, Different prime ideals in near-rings, Comm. Algebra 19 (1991), 2667–2675.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    C. B. Huijsmans and B. de Pagter, Ideal theory in f-algebras, Trans. Amer. Math. Soc. 269 (1982), 225–245.MathSciNetMATHGoogle Scholar
  7. 7.
    G. Mason, Reflexive ideals, Comm. Algebra 9 (1981), 1709–1724.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    G. Mason and R. Raphael, A propos des idéaux locaux; corrigendum et addendum., Ann. Sci. Math. Quebec 12 (1988), 255–261.MathSciNetMATHGoogle Scholar
  9. 9.
    M. Parmenter and S. Stewart, Normal rings and local ideals, Math. Scand. 60 (1987), 5–8.MathSciNetMATHGoogle Scholar
  10. 10.
    G. Pilz, Near-rings (2nd Ed.), North-Holland, Amsterdam, 1983.MATHGoogle Scholar
  11. 11.
    N. K. Thakare and S. K. Nimbhorkar, Space of minimal prime ideals of a ring without nilpotent elements, J. Pure Appl. Alg. 27, (1983), 75–85.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1996

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of New BrunswickFrederictonCanada

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