Kyungpook Mathematical Journal

  • 제54권3호
  • /
  • Pages.501-509
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  • 2014
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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The Order of Normal Form Generalized Hypersubstitutions of Type τ = (2)

  • 투고 : 2013.09.28
  • 심사 : 2013.04.15
  • 발행 : 2014.09.23
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초록

In 2000, K. Denecke and K. Mahdavi showed that there are many idempotent elements in $Hyp_{N_{\varphi}}(V)$ the set of normal form hypersubstitutions of type ${\tau}=(2)$ which are not idempotent elements in Hyp(2) the set of all hypersubstitutions of type ${\tau}=(2)$. They considered in which varieties, idempotent elements of Hyp(2) are idempotent elements of $Hyp_{N_{\varphi}}(V)$. In this paper, we study the similar problems on the set of all generalized hypersubstitutions of type ${\tau}=(2)$ and the set of all normal form generalize hypersubstitutions of type ${\tau}=(2)$ and determine the order of normal form generalize hypersubstitutions of type ${\tau}=(2)$.

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참고문헌

  1. K. Denecke, K. Mahdavi, The Order of Normal Form Hypersubstitutions of Type (2), Discussiones Mathematicae General Algebra and Applications, 20(2000), 183-192. https://doi.org/10.7151/dmgaa.1015
  2. K. Denecke, Sh. L. Wismath, Hyperidentities and clones, Gordon and Breach Sci. Publ., Amsterdam-Singapore(2000).
  3. S. Leeratanavalee, K. Denecke, Generalized Hypersubstitutions and Strongly Solid Varieties, In General and Applications, Proc. of "59th Workshop on General Algebra ", "15th Conference for Young Algebraists Potsdam 2000", Shaker Verlag(2000), 135-145.
  4. S. Leeratanavalee, S. Phatchat, Pre-Strongly Solid and Left-Edge (Right-Edge)-Strongly Solid Varieties of Semigroups, International Journal of Algebra, 1(5)(2007), 205-226. https://doi.org/10.12988/ija.2007.07021
  5. J. P lonka, Proper and Inner Hypersubstitutions of Varieties, In proceedings of the International Conference : Summer School on General Algebra and Ordered Set 1994, Palacky University Olomouc (1994), 106-115.
  6. W. Puninagool, S. Leeratanavalee, The Order of Generalized Hypersubstitutions of Type ${\tau}$ = (2), International Journal of Mathematics and Mathematical Science, Vol. 2008, Article ID 263541, 8 pages,doi:10.1155/2008/263541.