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Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup

Received: 1 January 2015     Accepted: 21 January 2015     Published: 1 February 2015
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Abstract

In this paper we find a relationship between r2(S) and r2(S⁄ρ) where S is a finite semigroup, ρis a congruence on S and S /ρis the quotient semigroup (/S/ ≥ 2and/ S⁄ρ/ ≥ 2). We also determine r5(S⁄ρ) under certain conditions. Moreover we find prime subsets of S/ρ.

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 1)
DOI 10.11648/j.pamj.20150401.13
Page(s) 24-25
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Rank, Prime Subset, Congruence, Independent Set

References
[1] John Macintosh H. and Maria Isabel R. “Rank Properties in Finite Semigroups”, Communications in Algebra, Vol 27 (11), pp. 5333-5347, 1999.
[2] John Macintosh H. and Maria Isabel R. “Rank Properties in Finite Semigroups II: The Small Rank and The Large Rank”, Southeast Asian Bulletin of Math.,Vol24, pp. 231-237, 2000.
[3] John Macintosh H. Foundations of SemigroupTheory, Clarendon Press, Oxford, 1995.
[4] Melis M. “Ranks of Certain Semigroups”, Semigroup Forum, Vol 28, pp. 99-105, 2009.
[5] Fikret K. “Relations Between Ranks of Certain Semigroups”, Selçuk J. Of Applied Math., Vol. 12, No 1, pp. 123-126, 2011.
[6] Jitender K. and Krishna K.V. “The Large Rank of a Finite Semigroup Using Prime Subsets”, Semigroup Forum, DOI 10.1007/s00233-014-9577-0.
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  • APA Style

    Melis Minisker. (2015). Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup. Pure and Applied Mathematics Journal, 4(1), 24-25. https://doi.org/10.11648/j.pamj.20150401.13

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    ACS Style

    Melis Minisker. Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup. Pure Appl. Math. J. 2015, 4(1), 24-25. doi: 10.11648/j.pamj.20150401.13

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    AMA Style

    Melis Minisker. Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup. Pure Appl Math J. 2015;4(1):24-25. doi: 10.11648/j.pamj.20150401.13

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  • @article{10.11648/j.pamj.20150401.13,
      author = {Melis Minisker},
      title = {Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {1},
      pages = {24-25},
      doi = {10.11648/j.pamj.20150401.13},
      url = {https://doi.org/10.11648/j.pamj.20150401.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150401.13},
      abstract = {In this paper we find a relationship between r2(S) and r2(S⁄ρ) where S is a finite semigroup, ρis a congruence on S and S /ρis the quotient semigroup (/S/ ≥ 2and/ S⁄ρ/ ≥ 2). We also determine r5(S⁄ρ) under certain conditions. Moreover we find prime subsets of S/ρ.},
     year = {2015}
    }
    

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    AU  - Melis Minisker
    Y1  - 2015/02/01
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    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
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    UR  - https://doi.org/10.11648/j.pamj.20150401.13
    AB  - In this paper we find a relationship between r2(S) and r2(S⁄ρ) where S is a finite semigroup, ρis a congruence on S and S /ρis the quotient semigroup (/S/ ≥ 2and/ S⁄ρ/ ≥ 2). We also determine r5(S⁄ρ) under certain conditions. Moreover we find prime subsets of S/ρ.
    VL  - 4
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Author Information
  • Mustafa Kemal University, Department of Mathematics, Antakya, Hatay, Turkey

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