On residual variables and stably polynomial algebras

Bhatwadekar, S. M. ; Dutta, Amartya K. (1993) On residual variables and stably polynomial algebras Communications in Algebra, 21 (2). pp. 635-645. ISSN 0092-7872

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Related URL: http://dx.doi.org/10.1080/00927879308824585


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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