arXiv
Open Access
2015
Families of Gorenstein and almost Gorenstein rings
Valentina Barucci
Marco D'Anna
Francesco Strazzanti
Abstrak
Starting with a commutative ring $R$ and an ideal $I$, it is possible to define a family of rings $R(I)_{a,b}$, with $a,b \in R$, as quotients of the Rees algebra $\oplus_{n \geq 0} I^nt^n$; among the rings appearing in this family we find Nagata's idealization and amalgamated duplication. Many properties of these rings depend only on $R$ and $I$ and not on $a,b$; in this paper we show that the Gorenstein and the almost Gorenstein properties are independent of $a,b$. More precisely, we characterize when the rings in the family are Gorenstein, complete intersection, or almost Gorenstein and we find a formula for the type.
Topik & Kata Kunci
Penulis (3)
V
Valentina Barucci
M
Marco D'Anna
F
Francesco Strazzanti
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2015
- Bahasa
- en
- Sumber Database
- arXiv
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- Open Access ✓