On the Star Class Group of a Pullback
| dc.creator | Fontana, Marco | |
| dc.creator | Park, Mi Hee | |
| dc.date | 2005-09-20 | |
| dc.date.accessioned | 2026-07-07T06:18:21Z | |
| dc.date.available | 2026-07-07T06:18:21Z | |
| dc.description | For the domain $R$ arising from the construction $T, M,D$, we relate the star class groups of $R$ to those of $T$ and $D$. More precisely, let $T$ be an integral domain, $M$ a nonzero maximal ideal of $T$, $D$ a proper subring of $k:=T/M$, $ϕ: T\to k$ the natural projection, and let $R=ϕ^{-1}(D)$. For each star operation $\ast$ on $R$, we define the star operation $\ast_ϕ$ on $D$, i.e., the ``projection'' of $\ast$ under $ϕ$, and the star operation ${(\ast)}_{_{T}}$ on $T$, i.e., the ``extension'' of $\ast$ to $T$. Then we show that, under a mild hypothesis on the group of units of $T$, if $\ast$ is a star operation of finite type, $0\to \Cl^{\ast_ϕ}(D) \to \Cl^\ast(R) \to \Cl^{{(\ast)}_{_{T}}}(T)\to 0$ is split exact. In particular, when $\ast = t_{R}$, we deduce that the sequence $ 0\to \Cl^{t_{D}}(D) {\to} \Cl^{t_{R}}(R) {\to}\Cl^{(t_{R})_{_{T}}}(T) \to 0 $ is split exact. The relation between ${(t_{R})_{_{T}}}$ and $t_{T}$ (and between $\Cl^{(t_{R})_{_{T}}}(T)$ and $\Cl^{t_{T}}(T)$) is also investigated. | |
| dc.description | J. Algebra (to appear) | |
| dc.identifier | https://arxiv.org/abs/math/0509456 | |
| dc.identifier | http://arxiv.org/abs/math/0509456 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94709 | |
| dc.subject | Commutative Algebra | |
| dc.title | On the Star Class Group of a Pullback | |
| dc.type | text |