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Primary elements in Prüfer lattices

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Abstract

In this paper we study primary elements in Prüfer lattices and characterize α-lattices in terms of Prüfer lattices. Next we study weak ZPI-lattices and characterize almost principal element lattices and principal element lattices in terms of ZPI-lattices.

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References

  1. D. D. Anderson: Abstract commutative ideal theory without chain condition. Algebra Universalis 6 (1976), 131–145.

    Google Scholar 

  2. D. D. Anderson, J. Matijevic and W. Nichols: The Krull intersection theorem II. Pacific J. Math. 66 (1976), 15–22.

    Google Scholar 

  3. D. D. Anderson, C. Jayaram and P.A. Phiri: Bear lattices. Acta. Sci. Math. (Szeged) 59 (1994), 61–74.

    Google Scholar 

  4. D. D. Anderson and E.W. Johnson: Dilworth's principal elements. Algebra Universalis 36 (1996), 392–404.

    Google Scholar 

  5. D. D. Anderson and C. Jayaram: Principal element lattices. Czechoslovak Math. J. 46(121) (1996), 99–109.

    Google Scholar 

  6. H. S. Butts and W. Smith: Prüfer rings. Math. Z. 95 (1967), 196–211.

    Google Scholar 

  7. R. P. Dilworth: Abstract commutative ideal theory. Pacific J. Math. 12 (1962), 481–498.

    Google Scholar 

  8. C. Jayaram and E. W. Johnson: Almost principal element lattices. Internat. J. Math. Math. Sci. 18 (1995), 535–538.

    Google Scholar 

  9. C. Jayaram and E. W. Johnson: s-prime elements in multiplicative lattices. Period. Math. Hungar. 31 (1995), 201–208.

    Google Scholar 

  10. C. Jayaram and E. W. Johnson: Some results on almost principal element lattices. Period. Math. Hungar. 31 (1995), 33–42.

    Google Scholar 

  11. C. Jayaram and E. W. Johnson: Primary elements and prime power elements in multiplicative lattices. Tamkang J. Math. 27 (1996), 111–116.

    Google Scholar 

  12. C. Jayaram and E. W. Johnson: Dedekind lattices. Acta. Sci. Math. (Szeged) 63 (1997), 367–378.

    Google Scholar 

  13. C. Jayaram and E. W. Johnson: σ-elements in multiplicative lattices. Czechoslovak Math. J. 48(123) (1998), 641–651.

    Google Scholar 

  14. E. W. Johnson and J. P. Lediaev: Representable distributive Noether lattices. Pacific J. Math. 28 (1969), 561–564.

    Google Scholar 

  15. P. J. McCarthy: Arithmetical rings and multiplicative lattices. Ann. Math. Pura. Appl. 82 (1969), 267–274.

    Google Scholar 

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Jayaram, C. Primary elements in Prüfer lattices. Czechoslovak Mathematical Journal 52, 585–593 (2002). https://doi.org/10.1023/A:1021731930659

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  • DOI: https://doi.org/10.1023/A:1021731930659

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