Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493241 | Journal of Algebra | 2005 | 24 Pages |
Abstract
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, Ï:Tâk the natural projection, and let R=Ïâ1(D). For each star operation * on R, we define the star operation *Ï on D, i.e., the “projection” of * under Ï, and the star operation (*)T on T, i.e., the “extension” of * to T. Then we show that, under a mild hypothesis on the group of units of T, if * is a star operation of finite type, then the sequence of canonical homomorphisms 0âCl*Ï(D)âCl*(R)âCl(*)T(T)â0 is split exact. In particular, when *=tR, we deduce that the sequence 0âCltD(D)âCltR(R)âCl(tR)T(T)â0 is split exact. The relation between (tR)T and tT (and between Cl(tR)T(T) and CltT(T)) is also investigated.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marco Fontana, Mi Hee Park,