The Derksen invariant vs. the Makar-Limanov invariant
نویسندگان
چکیده
منابع مشابه
Infinitely Generated Derksen and Makar-limanov Invariant *
In this paper, we give an example of a finitely generated 3-dimensional C-algebra which has infinitely generated Derksen invariant as well as MakarLimaonv invariant.
متن کاملAffine Surfaces with Trivial Makar-limanov Invariant
We study the class of 2-dimensional affine k-domainsR satisfying ML(R) = k, where k is an arbitrary field of characteristic zero. In particular, we obtain the following result: Let R be a localization of a polynomial ring in finitely many variables over a field of characteristic zero. If ML(R) = K for some field K ⊂ R such that trdeg K R = 2, then R is K-isomorphic to K[X, Y, Z]/(XY − P (Z)) fo...
متن کاملOn the Makar-limanov, Derksen Invariants, and Finite Automorphism Groups of Algebraic Varieties
A simple method of constructing a big stock of algebraic varieties with trivial Makar-Limanov invariant is described, the Derksen invariant of some varieties is computed, the generalizations of the Makar-Limanov and Derksen invariants are introduced and discussed, and some results on the Jordan property of automorphism groups of algebraic varieties are obtained.
متن کاملm at h . A G ] 2 8 Ju n 20 07 Constructing ( almost ) rigid rings and a UFD having infinitely generated Derksen and Makar - Limanov invariant
An example is given of a UFD which has 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. AMS classification: 14R20, 13A50, 13N15.
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It is proved that over every countable field K there is a nil algebra R such that the algebra obtained from R by extending the field K contains noncommutative free subalgebras of arbitrarily high rank. It is also shown that over every countable field K there is an algebra R without noncommutative free subalgebras of rank two such that the algebra obtained from R by extending the field K contain...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-07155-7