References
- Abhyankar, S. S., Eakin, P., Heinzer, W. (1972). On the uniqueness of the coefficient ring in a polynomial ring. J. Algebra 23(2):310–342. DOI: https://doi.org/10.1016/0021-8693(72)90134-2.
- Asanuma, T. (1987). Polynomial fibre rings of algebras over Noetherian rings. Invent. Math. 87(1):101–127. DOI: https://doi.org/10.1007/BF01389155.
- Asanuma, T., Bhatwadekar, S. M. (1997). Structure of A2-fibrations over one-dimensional Noetherian domains. J. Pure Appl. Algebra 115(1):1–13.
- Babu, J. R., Das, P. (2021). Structure of A2-fibrations having fixed point free locally nilpotent derivations. J. Pure Appl. Algebra 225(12):106763.
- Bass, H., Connell, E. H., Wright, D. L. (1976). Locally polynomial algebras are symmetric algebras. Invent. Math. 38(3):279–299. DOI: https://doi.org/10.1007/BF01403135.
- Bhatwadekar, S. M., Dutta, A. K. (1993). On residual variables and stably polynomial algebras. Commun. Algebra 21(2):635–645. DOI: https://doi.org/10.1080/00927879308824585.
- Bhatwadekar, S. M., Dutta, A. K. (1994). On affine fibrations. In Commutative Algebra (Trieste, 1992), River Edge, NJ: World Science Publication, pp. 1–17.
- Daigle, D. (1996). A necessary and sufficient condition for triangulability of derivations of k[X,Y,Z]. J. Pure Appl. Algebra 113(3):297–305.
- Daigle, D., Freudenburg, G. (1998). Locally nilpotent derivations over a UFD and an application to rank two locally nilpotent derivations of k[x1,…,xn]. J. Algebra 204(2):353–371.
- Das, P., Dutta, A. K. (2014). A note on residual variables of an affine fibration. J. Pure Appl. Algebra 218(10):1792–1799. DOI: https://doi.org/10.1016/j.jpaa.2014.02.005.
- Dutta, A. K., Gupta, N. (2015). The epimorphism theorem and its generalizations. J. Algebra Appl. 14(9):1540010. DOI: https://doi.org/10.1142/S0219498815400101.
- Eakin, P., Heinzer, W. (1973). A cancellation problem for rings. In Conference on commutative algebra (Univ. Kansas, Lawrence, Kan., 1972) (Lecture Notes in Math., Vol. 311). Berlin: Springer, pp. 61–77..
- El Kahoui, M., Ouali, M. (2014). The cancellation problem over Noetherian one-dimensional domains. Kyoto J. Math. 54(1):157–165. DOI: https://doi.org/10.1215/21562261-2400301.
- Freudenburg, G. (1995). Triangulability criteria for additive group actions on affine space. J. Pure Appl. Algebra 105(3):267–275. DOI: https://doi.org/10.1016/0022-4049(96)87756-5.
- Freudenburg, G. (2009). Derivations of R[X,Y,Z] with a slice. J. Algebra 322(9):3078–3087.
- Freudenburg, G. (2017). Algebraic Theory of Locally Nilpotent Derivations, Volume 136 of Encyclopedia of Mathematical Sciences (Invariant Theory and Algebraic Transformation Groups, VII). 2nd ed. Berlin: Springer-Verlag.
- Fujita, T. (1979). On Zariski problem. Proc. Japan Acad. Ser. A Math. Sci. 55(3):106–110. DOI: https://doi.org/10.3792/pjaa.55.106.
- Gupta, N. (2014). On the family of affine threefolds xmy=F(x,z,t). Compos. Math. 150(6):979–998.
- Hamann, E. (1975). On the R-invariance of R[X]. J. Algebra 35:1–16.
- Hochster, M. (1972). Nonuniqueness of coefficient rings in a polynomial ring. Proc. Amer. Math. Soc. 34(1):81–82. DOI: https://doi.org/10.1090/S0002-9939-1972-0294325-3.
- Kambayashi, T. (1975). On the absence of nontrivial separable forms of the affine plane. J. Algebra 35(1-3):449–456. DOI: https://doi.org/10.1016/0021-8693(75)90058-7.
- Keshari, M. K., Lokhande, S. A. (2014). A note on rigidity and triangulability of a derivation. J. Commut. Algebra 6(1):95–100. DOI: https://doi.org/10.1216/JCA-2014-6-1-95.
- Miyanishi, M. (2007). Recent developments in affine algebraic geometry: from the personal viewpoints of the author. In: Hibi, T., ed., Affine Algebraic Geometry. Osaka: Osaka University Press, pp. 307–378.
- Miyanishi, M., Sugie, T. (1980). Affine surfaces containing cylinderlike open sets. J. Math. Kyoto Univ. 20(1):11–42.
- Raynaud, M. (1968). Modules projectifs universels. Invent. Math. 6(1):1–26. DOI: https://doi.org/10.1007/BF01389829.
- Sathaye, A. (1983). Polynomial ring in two variables over a DVR: a criterion. Invent. Math. 74(1):159–168. DOI: https://doi.org/10.1007/BF01388536.
- van den Essen, A. (2007). Around the cancellation problem. In Affine Algebraic Geometry, Pages. Osaka: Osaka Univ. Press, p. 463–481.
- van den Essen, A., van Rossum, P. (2001). A class of counterexamples to the cancellation problem for arbitrary rings. Ann. Polon. Math. 76(1-2):89–93. (Polynomial automorphisms and related topics (Kraków, 1999)). DOI: https://doi.org/10.4064/ap76-1-8.
- Vénéreau, S., (2001). Automorphismes et variables de ľanneau de polynômes A[y1,y2,…,yn]. Ph.D. Thesis. Institut Fourier des mathématiques, Grenoble.
- Veĭsfeĭler, B. J., Dolgačev, I. V. (1974). Unipotent group schemes over integral rings. Izv. Akad. Nauk SSSR Ser. Mat. 38:757–799.
- Winkelmann, J. (1990). On free holomorphic C-actions on Cn and homogeneous Stein manifolds. Math. Ann. 286(1–3):593–612.
- Wright, D. (1981). On the Jacobian conjecture. Illinois J. Math. 25(3):423–440. DOI: https://doi.org/10.1215/ijm/1256047158.