Perinormalitas di Daerah Krull (Perinormality on Krull Domains)

https://doi.org/10.22146/jmt.47469

Qonita Qurrota A'yun(1*), Sri Wahyuni(2)

(1) Universitas Gadjah Mada
(2) Universitas Gadjah Mada
(*) Corresponding Author

Abstract


Daerah integral R dikatakan perinormal jika untuk setiap overring (lokal) T dari R yang memenuhi kondisi going-down, maka T merupakan lokalisasi dari R pada ideal prima. Perinormalitas merupakan salah satu sifat ketertutupan integral. Dengan memperhatikan bahwa klosur integral dari daerah normal Noether merupakan daerah Krull, akan ditunjukkan bagaimana sifat perinormalitas di daerah Krull.

An integral domain R is said to be perinormal if whenever T is a (local) overring of R such that the inclusion R in T satisfies going-down, it follows that T is a localization of R necessarily at a prime ideal. Perinormality is one of integral closedness property. As the integral closure of any Noetherian normal domain is Krull, it will be shown how perinormality behaves on Krull domains.


Full Text:

PDF Qonita


References

Cohen, I. S., and Seidenberg, A., Prime ideals and integral dependence, “Bull. Amer. Math. Soc.”, 110 (1946), pp 196-212.

Epstein, N., and Saphiro, J., Perinormality — a generalization of Krull domains, “Journal of Algebra”, 451 (2016), pp 65-84.

Fossum, R. M., The Divisor Class Group of a Krull Domain, “Ergebnisse dee Mathematik und ihrer Grenzgebiete”, vol. 74, Springer-Verlag, New York, Heidelberg, 1974.

Goldman, O., On a special class of Dedekind domains, “Topology”, 3 (1964), pp 113-118.

Gilmer, R., Multiplicative ideal theory, “Pure and Applied Mathematics”, vol. 90, Queen's Paper, Kingston Ontario, 1992.

Isaacs, M. I., “Algebra: A Graduate Course”, Brooks-Cole Publishing, 1994.

Larsen, M. D., and McCarthy, P. J., “Multiplicative Theory of Ideals”, vol. 43, Academic Press, New York and London, 1971.

Matsumura, H., “Commutative Ring Theory”, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge Univ. Press, Cambridge, 1986.



DOI: https://doi.org/10.22146/jmt.47469

Article Metrics

Abstract views : 1488 | views : 1197

Refbacks

  • There are currently no refbacks.


Jumlah Kunjungan: View My Stats