Öz
In this work, the set of quasi-primary ideals of a commutative ring with identity is equipped with a topology and is called the quasi-primary spectrum. Some topological properties of this space are examined. Further, a sheaf of rings on the quasi-primary spectrum is constructed and it is shown that this sheaf is the direct image sheaf with respect to the inclusion map from the prime spectrum of a ring to the quasi-primary spectrum of the same ring.
Anahtar Kelimeler
Quasi-primary ideals Quasi-primary spectrum Sheaf of rings Zariski topology
Kaynakça
- [1] Shafarevich I. R., 2013. Basic Algebraic Geometry 2: Schemes and Complex Manifolds, Third Edition, Springer-Verlag, Berlin.
- [2] Ueno K., 1999. Algebraic Geometry 1: From Algebraic Varieties to Schemes, Translations of Mathematical Monographs, Vol. 185, American Mathematical Society.
- [3] Hartshorne R., 2000. Algebraic Geometry, Springer Science+Business Media, LLC, New York.
- [4] Özkirişci N. A., Kılıç Z., Koç S., 2018. A Note on Primary Spectrum over Commutative Rings, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 64, pp. 111-120.
- [5] Fuchs L., 1947. On Quasi-primary Ideals, Acta Sci. Math. (Szeged), 11(3), pp. 174-183.
- [6] Sharp R. Y., 2001. Steps in Commutative Algebra, Second Edition, Cambridge University Press.
- [7] Atiyah M. F., MacDonald I. G., 1969. Introduction to Commutative Algebra, Addison-Wesley Publishing Company, Inc., London.
Öz
Kaynakça
- [1] Shafarevich I. R., 2013. Basic Algebraic Geometry 2: Schemes and Complex Manifolds, Third Edition, Springer-Verlag, Berlin.
- [2] Ueno K., 1999. Algebraic Geometry 1: From Algebraic Varieties to Schemes, Translations of Mathematical Monographs, Vol. 185, American Mathematical Society.
- [3] Hartshorne R., 2000. Algebraic Geometry, Springer Science+Business Media, LLC, New York.
- [4] Özkirişci N. A., Kılıç Z., Koç S., 2018. A Note on Primary Spectrum over Commutative Rings, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 64, pp. 111-120.
- [5] Fuchs L., 1947. On Quasi-primary Ideals, Acta Sci. Math. (Szeged), 11(3), pp. 174-183.
- [6] Sharp R. Y., 2001. Steps in Commutative Algebra, Second Edition, Cambridge University Press.
- [7] Atiyah M. F., MacDonald I. G., 1969. Introduction to Commutative Algebra, Addison-Wesley Publishing Company, Inc., London.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 11 Ekim 2023 |
| Yayımlanma Tarihi | 30 Kasım 2023 |
| Kabul Tarihi | 3 Haziran 2022 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 6 Sayı: 2 |