Constructing (Almost) Rigid Rings and a UFD Having Infinitely Generated Derksen and Makar-Limanov Invariants
Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 77-86

Voir la notice de l'article provenant de la source Cambridge University Press

An example is given of a UFD which has an infinitely generated Derksen invariant. The ring is “almost rigid” meaning that the Derksen invariant is equal to the Makar-Limanov invariant. Techniques to show that a ring is (almost) rigid are discussed, among which is a generalization of Mason's ABC-theorem.
DOI : 10.4153/CMB-2010-017-8
Mots-clés : 14R20, 13A50, 13N15
Finston, David; Maubach, Stefan. Constructing (Almost) Rigid Rings and a UFD Having Infinitely Generated Derksen and Makar-Limanov Invariants. Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 77-86. doi: 10.4153/CMB-2010-017-8
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[1] [1] de Bondt, M., Another generalisation of Mason's ABC-theorem. arXiv:math.GM0707.0434v2. Google Scholar

[2] [2] Crachiola, A., On the AK-Invariant of Certain Domains. Ph.D. thesis, Wayne State University, May 2004. Google Scholar

[3] [3] Crachiola, A. and Makar-Limanov, L., On the rigidity of small domains. J. Algebra 284(2005), no. 1, 1–12. doi:10.1016/j.jalgebra.2004.09.015 Google Scholar

[4] [4] Deveney, J. K. and Finston, D. R., Ga-actions on ℂ3 and ℂ7 . Comm. Algebra 22(1994), 6295–6302. doi:10.1080/00927879408825190 Google Scholar

[5] [5] van den Essen, A., Polynomial Automorphisms and the Jacobian Conjecture. Progress in Mathematics 190. Birkhäuser-Verlag, Basel, 2000. Google Scholar

[6] [6] Finston, D. and Maubach, S., The automorphism group of certain factorial threefolds and a cancellation problem. Israel J. Math. 163(2008), 369–381. doi:10.1007/s11856-008-0016-3 Google Scholar

[7] [7] Fossum, R., The Divisor Class Group of a Krull Domain. Ergebniss der Mathematik und ihrer Grenzgebiete 74. Springer-Verlag, New York, 1973. Google Scholar

[8] [8] Freudenburg, G., Algebraic Theory of Locally Nilpotent Derivations, Encyclopaedia of Mathematical Sciences 136. Springer-Verlag, Berlin, 2006. Google Scholar

[9] [9] Gurjar, R V., Masuda, K., Miyanishi, M., and Russell, P., Affine lines on affine surfaces and the Makar-Limanov invariant. Canad. J. Math. 60(2008), no. 1, 109–139. doi:10.4153/CJM-2008-005-8 Google Scholar

[10] [10] Hartshorne, R. and Ogus, A., On the factoriality of local rings of small embedding codimension. Comm. Algebra 1(1974), 415–437. doi:10.1080/00927877408548627 Google Scholar

[11] [11] Makar-Limanov, L., Again x + x 2 y + z 2 + t 3 = 0 . In: Affine Algebraic Geometry. Contemp. Math. 369. American Mathematical Society, Providence, RI, 2005, pp. 177–182. Google Scholar

[12] [12] Maubach, S., Hilbert's 14th Problem and Related Topics. Master's thesis, University of Nijmegen, 1998. Google Scholar

[13] [13] Masuda, K. and Miyanishi, M., Étale endomorphisms of algebraic surfaces with actions. Math. Ann. 319(2001) no. 3, 493–516. doi:10.1007/PL00004445 Google Scholar

[14] [14] Maubach, S., Infinitely generated Derksen and Makar-Limanov invariant. Osaka J. Math. 44(2007), no. 4, 883–886. Google Scholar

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