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Kernel ideals and cokernel filters of a p-algebra

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Abstract

We discuss congruences of p-algebras. We characterize kernel ideals of a p-algebra. Indeed, we show that an ideal of a p-algebra is a p-ideal if and only if it is a kernel ideal. We study cokernel filters of a p-algebra. We construct a class of p-algebras in which every cokernel filter is a p-filter. We also give some characterizations of Boolean congruences of a p-algebra.

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References

  1. Begum S.N., Noor A.S.A.: Congruence kernels of distributive PJP-semilattices. Math. Bohem. 136, 225–239 (2011)

    MathSciNet  MATH  Google Scholar 

  2. Begum S.N., Noor A.S.A., Talukder M.R.: Kernel ideals of a Stone JP-semilattice. Acta Math. Hungar. 140, 1–11 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Blyth T.S.: Ideals and filters of pseudo-complemented semilattices. Proc. Edinburgh Math. Soc. 23, 301–316 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Grätzer, Lattice Theory: First Concepts and Distributive Lattices, W. H. Freeman (San Francisco, 1971).

  5. G. Grätzer, General Lattice Theory, Birkhäuser Verlag (Basel, 1998).

  6. Cornish W.H.: Congruences on distributive pseudo-complemented lattices. Bull. Austral. Math. Soc. 82, 161–179 (1973)

    Article  MATH  Google Scholar 

  7. T. Katriňák, P-algebras, in: Contributions to lattice theory, Szeged, 1980, Colloq. Math. Soc. János Bolyai, 33 (1983), pp. 549–573.

  8. Katriňák T., Mederly P.: Construction of modular p-algebras. Algebra Universalis 4, 301–315 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  9. Katriňák T., Mederly P.: Construction of p-algebras. Algebra Universalis 17, 288–316 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  10. C. Nag, S. N. Begum and M. R. Talukder, P-ideals and p-filters of a p-algebra, Southeast Asian Bull. Math., accepted.

  11. Rav Y.: Semi prime ideals in general lattices. J. Pure Appl. Algebra 56, 105–118 (1989)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, 3114, Bangladesh

    S. N. Begum, C. Nag & M. R. Talukder

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  1. S. N. Begum
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  2. C. Nag
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  3. M. R. Talukder
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Correspondence to M. R. Talukder.

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Begum, S.N., Nag, C. & Talukder, M.R. Kernel ideals and cokernel filters of a p-algebra. Acta Math. Hungar. 154, 279–288 (2018). https://doi.org/10.1007/s10474-018-0793-z

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  • DOI: https://doi.org/10.1007/s10474-018-0793-z

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