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Ideals of the Multiplicative Semigroups ℤn and their Products

Puninagool, Wattapong;Sanwong, Jintana

  • Received : 2007.11.14
  • Accepted : 2008.06.09
  • Published : 2009.03.31

Abstract

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.

Keywords

ideals;integers modulo n;product semigroups

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