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...

Abstract We study subfields of quotient division algebras of domains of finite GK dimension and introduce a combinatorial property we call the straightening property. We show that many classes of algebras have this straightening property and show that if A is a domain of GK dimension d with this property that is not PI, then the maximal subfields of the quotient division algebra of A have trans...

Using methods of higher algebraic K-theory, van der Kallen proved that SLn(F [x]) does not have bounded word length with respect to elementary matrices if the field F has infinite transcendence degree over its prime subfield. A short explicit proof of this result is exhibited by constructing a sequence of matrices with infinitely growing word length. This construction is also used to show that ...

We prove that the types in Separably Closed Hasse Fields which have transcendence degree 1 are separably thin

The relationship of parenting styles with adolescents' outcomes was analyzed within a sample of Spanish adolescents. A sample of 1456 teenagers from 13 to 16 years of age, of whom 54.3% were females, reported on their parents' child-rearing practices. The teenagers' parents were classified into one of four groups (authoritative, authoritarian, indulgent, or neglectful). The adolescents were the...

We classify projective planes in algebraic combinatorial geometries in arbitrary fields of characteristic zero. We investigate the first-order theories of such geometries and pregeometries. Then we classify the algebraic combinatorial geometries of arbitrary field extensions of the transcendence degree ≥ 5 and describe their groups of automorphisms. Our results and proofs extend similar results...

art of Kant’s reason for writing the first Critique is to show the limits of theoretical reason; one of these limits is its inability to experience transcendence, to cognize supersensible objects, to intuit the sublime. But Kant doesn’t thereby want to make these experiences impossible—indeed, part of his reason for writing the second and third Critiques, along with such works as Religion withi...

Let K be a field, K[X] = K[X1, . . . , Xn] the polynomial ring in n variables over K for some n ∈ N, and K(X) the field of fractions of K[X]. Assume that L is a subfield of K(X) containing K. Then, the Fourteenth Problem of Hilbert asks whether the Ksubalgebra L ∩K[X] of K[X] is finitely generated. Zariski [17] showed in 1954 that the answer to this problem is affirmative if the transcendence d...

We investigate the amenability of skew field extensions of the complex numbers. We prove that all skew fields of finite Gelfand-Kirillov transcendence degree are amenable. However there are both amenable and non-amenable finitely generated skew fields of infinite Gelfand-Kirillov transcendence degree. AMS Subject Classifications: 12E15, 43A07