Journal of the Ramanujan Mathematical Society
Volume 40, Issue 4, December 2025 pp. 379–383.
Retracts of Laurent polynomial rings
Authors:
Neena Gupta and Takanori Nagamine
Author institution:Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India.
Summary:
Let R be an integral domain and B = R[x{1}, … , x{n}] be the polynomial
ring in n variables over R. In this paper, we consider an R-retract A of
B[1/M] for a monomial M in x{1}, … , x{n}. We show that, if either (1)
M = ∏{n}{i = 1} x{i}, or (2) R is a UFD and n ≤ 3, then there
exist a polynomial ring B′ = R[y1, … , yn] and a monomial M′ in y1,
… , yn such that A ≅{R} B′[1/M′]. In particular, every R-retract
of a Laurent polynomial ring over R is again a Laurent polynomial ring over
R.
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