A criterion to determine residual coordinates of $$\pmb {\mathbb {A}}^\textbf{2}$$ -fibrations
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Let $ A $ be a retract of the polynomial ring in three variables over a field $ k $. It is known
that if ${\rm char}\:(k)= 0$ or ${\rm tr. deg}\: _k A\not= 2$ then $ A $ is a polynomial ring. In …

Let $ R $ be an integral domain and $ B= R [x_1,\ldots, x_n] $ be the polynomial ring. In this
paper, we consider retracts of $ B [1/M] $ for a monomial $ M $. We show that (1) if …

arXiv:2212.03488v4 [math.AC] 14 Feb 2023 Page 1 A criterion to determine residual coordinates
of A2-fibrations Janaki Raman Babu Department of Mathematics, Indian Institute of Space …

Let k be a field of characteristic zero and B ak-domain. Let R be a retract of B being the
kernel of a locally nilpotent derivation of B. We show that if B= R⊕ I for some principal ideal I …