Anderson, D. D.; Mott, J. L.; Zafrullah, M. Finite character representations for integral domains. (English) Zbl 0773.13004 Boll. Unione Mat. Ital., VII. Ser., B 6, No. 3, 613-630 (1992). The authors give necessary and sufficient conditions in order that an integral domain \(D\) has a finite character representation \(\bigcap_{\text{ht}P=1}\{D_ P\}\). They prove, for example, that \(D\) has such a representation if and only if every proper principal ideal in \(D\) is a \(t\)-product of primary ideals, that is if and only if for every minimal prime ideal \(P\) in \(D\) over a proper principal ideal \((x)\), we have that \((x)_ P\cap D\) is \(t\)-invertible. This result is used to characterize some classes of integral domains. Finally the authors study when \(\bigcap_{P\in t-\text{Max}(D)}\{D_ P\}\) has finite character. Reviewer: E.Stagnaro (Padova) Cited in 1 ReviewCited in 50 Documents MSC: 13G05 Integral domains 13E15 Commutative rings and modules of finite generation or presentation; number of generators 13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) Keywords:factorial domains; discrete valuation rings; integral domain; finite character representation PDFBibTeX XMLCite \textit{D. D. Anderson} et al., Boll. Unione Mat. Ital., VII. Ser., B 6, No. 3, 613--630 (1992; Zbl 0773.13004)