Let A be a finitely generated domain of GK dimension less than 3 over a field K and let Q(A) denote the quotient division algebra of A. Using the ideas of Smoktunowicz, we show that if D is a finitely generated division subalgebras 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 dime...

Given an affine domain of Gelfand–Kirillov dimension 2 over an algebraically closed field, it is shown that the centralizer of any non-scalar element of this domain is a commutative domain of Gelfand–Kirillov dimension 1 whenever the domain is not polynomial identity. It is shown that the maximal subfields of the quotient division ring of a finitely graded Goldie algebra of Gelfand– Kirillov di...

The authors conducted this study to further validate the revised short form of the Gratitude, Resentment, and Appreciation Test by investigating the relationship between GRAT-measured gratitude and two other constructs: (a) spiritual transcendence and (b) materialism. As predicted, both the GRAT and its subscales correlated positively with a measure of spiritual transcendence and negatively wit...

The term self-transcendence has been used to refer both to a process of movement beyond one’s immediate self-boundaries, and to a quality which emerges as a result of this process, culminating in a broadened worldview. Self-transcendence has appeared as a key theme in several disciplines including transpersonal psychology, personality theory, and nursing theory. The scarcity of widely accepted ...

Article history: Received 4 April 2013 Available online 6 June 2013 Communicated by Leonard L. Scott, Jr. MSC: 34M15 34M03 12H20 35A24 33B20 20H20 37K20

The relation between parenting styles and adolescent outcomes was analyzed in a sample of 1,198 15-18-year-old Brazilians. The adolescents were classified into 1 of 4 groups (Authoritative, Authoritarian, Indulgent, and Neglectful) on the basis of their own ratings of their parents on two dimensions: Acceptance/ Involvement and Strictness/Imposition. The adolescents were then contrasted along t...

For a smooth complex projective variety X defined over a number field, we have filtrations on the Chow groups depending on the choice of realizations. If the realization consists of mixed Hodge structure without any additional structure, we can show that the obtained filtration coincides with the filtration of Green and Griffiths, assuming the Hodge conjecture. In the case the realizations cont...

We already met a number of open problems in these notes, in particular in § 1.1.1. We collect further conjectures in this field, but this is only a very partial list of questions which deserve to be investigated further. Part of this section if from [W 2004], especially § 3. When K is a field and k a subfield, we denote by trdegkK the transcendence degree of the extension K/k. In the case k = Q...

We study the p-adic valuation of the values of normalised Hecke eigenforms attached to non-isotrivial elliptic curves defined over function fields of transcendence degree one over finite fields of characteristic p. We derive upper bounds on the smallest attained valuation in terms of the minimal discriminant under a certain assumption on the function field and provide examples to show that our ...