Yanagihara, Hiroshi On an intrinsic definition of weakly normal rings. (English) Zbl 0586.13006 Kobe J. Math. 2, 89-98 (1985). Originally a commutative ring A was defined to be weakly normal (seminormal) if A was equal to its weak normalization (seminormalization). R. G. Swan [J. Algebra 67, 210-219 (1980; Zbl 0473.13001)] defined A to be seminormal if A is reduced and for any elements b, c in A with \(b^ 3=c^ 2\), there is an element a in A with \(a^ 2=b\) and \(a^ 3=c\). He showed that this definition agrees with the classical definition and gave a thorough investigation of seminormality. The purpose of this paper is to give a treatment of weakly normal rings along the lines of Swan’s treatment of seminormal rings. The intrinsic definition of weakly normal rings mentioned in the title is that A is weakly normal if A is seminormal and for any elements b, c, d, e in A with d a nonzero divisor with \(c^ p=bd^ p\) and \(pc=de\) for some prime p, there is an element a in A with \(b=a^ p\) and \(e=pa\). Reviewer: D.D.Anderson Cited in 1 ReviewCited in 11 Documents MSC: 13A99 General commutative ring theory 13B02 Extension theory of commutative rings Keywords:weakly normal extension; seminormality; weakly normal rings Citations:Zbl 0473.13001 PDFBibTeX XMLCite \textit{H. Yanagihara}, Kobe J. Math. 2, 89--98 (1985; Zbl 0586.13006)