ONE-DIMENSIONAL SEMILOCAL RINGS WITH RESIDUE DOMAINS OF PRESCRIBED CARDINALITIES

Authors
SHAH C
Citation
C. Shah, ONE-DIMENSIONAL SEMILOCAL RINGS WITH RESIDUE DOMAINS OF PRESCRIBED CARDINALITIES, Communications in algebra, 25(5), 1997, pp. 1641-1654
Citations number
8
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Communications in algebra → ACNP
ISSN journal
00927872
Volume
25
Issue
5
Year of publication
1997
Pages
1641 - 1654
Database
ISI
SICI code
0092-7872(1997)25:5<1641:OSRWRD>2.0.ZU;2-0
Abstract
We determine those pairs consisting of a partially ordered set U and a collection C of cardinal numbers which can occur as Spec(R) and the c ollection C(R) of cardinalities of residue domains of R, respectively, where R is a one-dimensional semilocal (Noetherian) ring. This result is used to characterize Spec(R[x]), the spectrum of the polynomial ri ng in one variable over a one-dimensional semilocal ring R.