an:03922815
Zbl 0577.13010
Arnold, J. T.
The catenarian property of power series rings over a Pr??fer domain
EN
Proc. Am. Math. Soc. 94, 577-580 (1985).
00148786
1985
j
13E99 13F25 13F05 13C15 13E15
valuation ring; strong finite type; SFT-property; Pr??fer domain; power series ring; catenarian
The author has defined previously an ideal A of a commutative ring R to be of strong finite type provided there is a finitely generated ideal B of R with \(B\subseteq A\) and a positive integer k such that \(a^ k\in B\) for each \(a\in A\); the ring R is said to have the SFT-property provided that each ideal of R is of strong finite type. This paper is concerned with a Pr??fer domain D that has the SFT-property: the main results are that the power series ring D[[X]] is catenarian, but that if \(n>1\) and dim D\(>1\) then the power series ring \(D[[X_ 1,...,X_ n]]\) is not catenarian.
R.Y.Sharp