Kyungpook Mathematical Journal

  • 제49권1호
  • /
  • Pages.41-46
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  • 2009
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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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Ideals of the Multiplicative Semigroups ℤn and their Products

  • 투고 : 2007.11.14
  • 심사 : 2008.06.09
  • 발행 : 2009.03.31
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초록

The multiplicative semigroups $\mathbb{Z}_n$ have been widely studied. But, the ideals of $\mathbb{Z}_n$ seem to be unknown. In this paper, we provide a complete descriptions of ideals of the semigroups $\mathbb{Z}_n$ and their product semigroups ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$. We also study the numbers of ideals in such semigroups.

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참고문헌

  1. G. Ehrlich, Unit-regular ring, Portugaliae Math., 27(1968), 209-212.
  2. E. Hewitt and H. S. Zuckerman, The multiplicative semigroup of integers modulo m, Pacific J. Math., 10(1960), 1291-1308. https://doi.org/10.2140/pjm.1960.10.1291
  3. E. Hewitt and H. S. Zuckerman, Finitely dimensional convolution algebras, Acta Math. 93(1955), 67-119. https://doi.org/10.1007/BF02392520
  4. J. M. Howie, An Introduction to Semigroup Theory, Academic Press, London, 1976.
  5. T. M. Hungerford, Algebra, Spring-Verlag, Newyork, 2003.
  6. Y. Kemprasit and S. Buapradist, A note on the multiplicative semigroup $Z_n$ whose bi-ideals are quasi-ideals, Southeast Asian Bull. Math., Springer-Verlag 25(2001), 269-271. https://doi.org/10.1007/s10012-001-0269-9
  7. A. E. Livingston and M. L. Livingston, The congruence $a^{r+s}{\equiv}a^r(mod\;m)$, Amer. Math. Monthly, 85(1980), 811-814.
  8. W. Sierpinski, Elementary Theory of Numbers, PWN-Polish Scientific Publisher, Warszawa, 1988.
  9. H. S. Vandiver and M. W. Weaver, Introduction to arithmetic factorization and congruences from the standpoint of abstract algebra, Amer. Math. Monthly, 65(1958), 48-51.