منابع مشابه
A ug 2 00 7 Division algebras of Gelfand - Kirillov transcendence degree 2 Jason
Let A be a finitely generated K-algebra that is a domain of GK dimension less than 3, and let Q(A) denote the quotient division algebra of A. We show that if D is a division subalgebra of Q(A) of GK dimension at least 2 then Q(A) is finite dimensional as a left D-vector space. We use this to show that if A is a finitely generated domain of GK dimension less than 3 over an algebraically closed f...
متن کاملSimple Algebras of Gelfand - Kirillov Dimension Two
Let k be a field. We show that a finitely generated simple Goldie k-algebra of quadratic growth is noetherian and has Krull dimension 1. Thus a simple algebra of quadratic growth is left noetherian if and only if it is right noetherian. As a special case, we see that if A is a finitely generated simple domain of quadratic growth then A is noetherian and by a result of Stafford every right and l...
متن کاملGelfand-Kirillov Dimension in some Crossed Products
Let k be a field, R a k-algebra and A = R[θ1, θ2, . . . , θn] a PoincaréBirkhoff-Witt extension of R. If each θi acts locally finitely on R, then we show that GKdim(A) = GKdim(R) + n. From this we deduce some results concerning incomparability, prime length and Tauvel’s height formula in the crossed product R?g where g is a finite-dimensional Lie algebra acting as derivations on R. Similar resu...
متن کاملLie Algebras with Finite Gelfand-kirillov Dimension
We prove that every finitely generated Lie algebra containing a nilpotent ideal of class c and finite codimension n has Gelfand-Kirillov dimension at most cn. In particular, finitely generated virtually nilpotent Lie algebras have polynomial growth.
متن کامل∗−orderings and ∗−valuations on Algebras of Finite Gelfand-kirillov Dimension
Considerable work has been done in developing the relationship between ∗-orderings, ∗valuations and the reduced theory of Hermitian forms over a skewfield with involution [12] [13] [14] [15] [16] [23] [24]. This generalizes the well-known theory in the commutative case; e.g., see [4] [6] [7] [27]. In the commutative theory, formally real function fields provide a rich source of examples [6]. In...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1996
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-96-01702-3