Cho, Yong-Hwan Pseudo-valuation domains. (English) Zbl 0945.13012 Commun. Korean Math. Soc. 11, No. 2, 281-284 (1996). From the paper: Let \(R\) be an integral domain with quotient field \(K\). A prime ideal \(P\) of \(R\) is said to be strongly prime if \(x,y \in K\) and \(xy\in P\) imply that \(x\in P\) or \(y\in P\). A domain \(R\) is called a pseudo-valuation domain (PVD) if each prime ideal of \(R\) is a strongly prime ideal. This concept of strongly prime ideals was introduced by J. R. Hedstrom and E. G. Houston [Pac. J. Math. 75, 137-147 (1978; Zbl 0368.13002)] in their study of pseudo valuation domains. In this short paper is generalize theorem 1.4 of the cited paper, that a quasi local domain is a PVD if and only if its maximal ideal is strongly prime. Cited in 1 Document MSC: 13F30 Valuation rings 13A15 Ideals and multiplicative ideal theory in commutative rings Keywords:integral domain; strongly prime ideal; pseudo-valuation domain Citations:Zbl 0368.13002; Zbl 0376.13001 PDFBibTeX XMLCite \textit{Y.-H. Cho}, Commun. Korean Math. Soc. 11, No. 2, 281--284 (1996; Zbl 0945.13012)