Gelfand-Kirillov dimension and associated graded modules
نویسندگان
چکیده
منابع مشابه
Simple 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...
متن کاملRe-filtering and Exactness of the Gelfand–kirillov Dimension
– We prove that any multi-filtered algebra with semi-commutative associated graded algebra can be endowed with a locally finite filtration keeping up the semi-commutativity of the associated graded algebra. As consequences, we obtain that Gelfand–Kirillov dimension is exact for finitely generated modules and that the algebra is finitely partitive. Our methods apply to algebras of current intere...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1989
ISSN: 0021-8693
DOI: 10.1016/0021-8693(89)90301-3