Examples in finite Gel′fand-Kirillov dimension II
نویسنده
چکیده
For any field F , we give an example of a prime finitely generated F -algebra of GK dimension 2 for which GK dimension is not finitely partitive. For each m ∈ {0, 1, 2, 3, . . .}∪{∞}, we give an example of a prime finitely generated F -algebra having GK dimension 2 which has classical Krull dimension m; the algebra of GK dimension 2 which has infinite classical Krull dimension has the additional property that it does not satisfy the ascending chain condition on prime ideals. This answers some questions of Bergman.
منابع مشابه
Examples in finite Gel′fand-Kirillov dimension
Abstract By modifying constructions of Bĕıdar and Small we prove that for countably generated prime F -algebras of finite GK dimension there exists an affinization having finite GK dimension. Using this result we show: for any field there exists a prime affine algebra of GK dimension two that is neither primitive nor PI; for any countable field F there exists a prime affine F -algebra of GK dim...
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 کامل9 M ay 2 00 5 An infinite dimensional affine nil algebra with finite Gelfand - Kirillov dimension ∗
We construct a nil algebra over a countable field which has finite but non-zero Gelfand-Kirillov dimension. 2000 Mathematics subject classification: 16N, 16P90.
متن کاملLeavitt Path Algebras of Finite Gelfand–kirillov Dimension
Groebner–Shirshov Basis and Gelfand–Kirillov dimension of the Leavitt path algebra are derived.
متن کاملThe Gelfand-kirillov Dimension of Quadratic Algebras Satisfying the Cyclic Condition
We consider algebras over a field K presented by generators x1, . . . , xn and subject to (n 2 ) square-free relations of the form xixj = xkxl with every monomial xixj , i = j, appearing in one of the relations. It is shown that for n > 1 the Gelfand-Kirillov dimension of such an algebra is at least two if the algebra satisfies the so-called cyclic condition. It is known that this dimension is ...
متن کامل