Araştırma Makalesi
Yıl 2017,
, 39 - 54, 17.01.2017
Öz
Let G be a subgroup of the automorphism group of a commutative
ring with identity T. Let R be a subring of T. We show that RG ⊂ T G
is a minimal ring extension whenever R ⊂ T is a minimal extension under
various assumptions. Of the two types of minimal ring extensions, integral
and integrally closed, both of these properties are passed from R ⊂ T to
RG ⊆ T G. An integrally closed minimal ring extension is a flat epimorphic
extension as well as a normal pair. We show that each of these properties also
pass from R ⊂ T to RG ⊆ T G under certain group action.
Anahtar Kelimeler
Kaynakça
- [6] D. E. Dobbs and J. Shapiro, Descent of divisibility properties of integral domains
- to fixed rings, Houston J. Math., 32(2) (2006), 337-353.
- [7] D. E. Dobbs and J. Shapiro, Descent of minimal overrings of integrally closed
- domains to fixed rings, Houston J. Math., 33(1) (2007), 59-82.
- [8] D. E. Dobbs and J. Shapiro, Transfer of Krull dimension, lying-over, and
- going-down to the fixed ring, Comm. Algebra, 35(4) (2007), 1227-1247.
- [9] D. Ferrand and J.-P. Olivier, Homomorphismes minimaux d’anneaux, J. Algebra,
- 16 (1970), 461-471.
- [10] M. Fontana, J. A. Huckaba and I. J. Papick, Pr¨ufer Domains, Monographs
- and Textbooks in Pure and Applied Mathematics, 203, Marcel Dekker, Inc.,
- New York, 1997.
- [11] I. Kaplansky, Commutative Rings, The University of Chicago Press, Chicago,
- Revised edition, 1974.
- [12] M. Knebusch and D. Zhang, Manis Valuations and Pr¨ufer Extensions I, Lecture
- Notes in Mathematics, 1791, Springer-Verlag, Berlin, 2002.
- [13] M. E. Manis, Valuations on a commutative ring, Proc. Amer. Math. Soc., 20
- (1969), 193-198
- [14] G. Picavet and M. Picavet-L’Hermitte, Multiplicative Ideal Theory in Commutative
- Algebra, Chapter About Minimal Morphisms, 369-386, Springer, New
- York, 2006.
- [15] B. Stenstr¨om, Rings of Quotients, Springer-Verlag, New York, Heidelberg
- Berlin, 1975.
Yıl 2017,
, 39 - 54, 17.01.2017
Öz
Kaynakça
- [6] D. E. Dobbs and J. Shapiro, Descent of divisibility properties of integral domains
- to fixed rings, Houston J. Math., 32(2) (2006), 337-353.
- [7] D. E. Dobbs and J. Shapiro, Descent of minimal overrings of integrally closed
- domains to fixed rings, Houston J. Math., 33(1) (2007), 59-82.
- [8] D. E. Dobbs and J. Shapiro, Transfer of Krull dimension, lying-over, and
- going-down to the fixed ring, Comm. Algebra, 35(4) (2007), 1227-1247.
- [9] D. Ferrand and J.-P. Olivier, Homomorphismes minimaux d’anneaux, J. Algebra,
- 16 (1970), 461-471.
- [10] M. Fontana, J. A. Huckaba and I. J. Papick, Pr¨ufer Domains, Monographs
- and Textbooks in Pure and Applied Mathematics, 203, Marcel Dekker, Inc.,
- New York, 1997.
- [11] I. Kaplansky, Commutative Rings, The University of Chicago Press, Chicago,
- Revised edition, 1974.
- [12] M. Knebusch and D. Zhang, Manis Valuations and Pr¨ufer Extensions I, Lecture
- Notes in Mathematics, 1791, Springer-Verlag, Berlin, 2002.
- [13] M. E. Manis, Valuations on a commutative ring, Proc. Amer. Math. Soc., 20
- (1969), 193-198
- [14] G. Picavet and M. Picavet-L’Hermitte, Multiplicative Ideal Theory in Commutative
- Algebra, Chapter About Minimal Morphisms, 369-386, Springer, New
- York, 2006.
- [15] B. Stenstr¨om, Rings of Quotients, Springer-Verlag, New York, Heidelberg
- Berlin, 1975.
Toplam 22 adet kaynakça vardır.
Ayrıntılar
| Konular | Matematik |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 17 Ocak 2017 |
| Yayımlandığı Sayı | Yıl 2017 |