On residual variables and stably polynomial algebras
Title:
On residual variables and stably polynomial algebras
Author:
Bhatwadekar, S.M. Dutta, Amartya K.
Appeared in:
Communications in algebra
Paging:
Volume 21 (1993) nr. 2 pages 635-645
Year:
1993
Contents:
Let R be a commutative noetherian ring and let R[X,Y] be a polynomial algebra in two variables over R. Let W be an element of R[X,Y]. In this paper we show that R[X,Y] is a stably polynomial algebra over R[W] if and only if W is a residual variable in R[X,Y]. Moreover, in this case, if either R contains the field of rationals or if Rred is seminormal, then W is a variable in R[X,Y].
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