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Ideals of the Multiplicative Semigroups Zn and their Products
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The multiplicative semigroups Zn have been widely studied. But, the ideals of Zn seem to be unknown. In this paper, we provide a complete descriptions of ideals of the semigroups Zn and their product semigroups Zm×Zn. We also study the numbers of ideals in such semigroups.
Abstract
The multiplicative semigroups Zn have been widely studied. But, the ideals of Zn seem to be unknown. In this paper, we provide a complete descriptions of ideals of the semigroups Zn and their product semigroups Zm×Zn. We also study the numbers of ideals in such semigroups.
참고문헌 (9)
- G. Ehrlich, "Unit-regular ring", Portugaliae Math., 27, pp.209~212 (1968)
- E. Hewitt, "The multiplicative semigroup of integers modulo", Pacific J. Math., 10, pp.1291~1308 (1960)
- E. Hewitt, "Finitely dimensional convolution algebras", ActaMath, 93, pp.67~119 (1955)
- J. M. Howie, "An Introduction to Semigroup Theory" (1976), Academic Press
- T. M. Hungerford, "Algebra" (2003), Spring-Verlag
- Y. Kemprasit, "A note on the multiplicative semigroup Zn whosebi-ideals are quasi-ideals", Southeast Asian Bull. Math., 25, pp.269~271 (2001), Springer-Verlag
- A. E. Livingston, "The congruence ar+s ar(mod m)", Amer. Math. Monthly, 85, pp.811~814 (1980)
- W. Sierpinski, "Elementary Theory of Numbers" (1988), PWN-Polish Scientific Publisher
- H. S. Vandiver, "Introduction to arithmetic factorization and con-gruences from the standpoint of abstract algebra", Amer. Math., 65, pp.48~51 (1958)
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