Hilbert’s fourteenth problem asks whether the ring of invariants of any representation of a linear algebraic group is finitely generated over the base field. Nagata gave the first counterexample, using a representation of (Ga) 13, where Ga denotes the additive group [22]. In his example, the representation is defined over a field of large transcendence degree over the prime field (of any charac...

Let D be a division ring with an involution and characteristic different from 2. Then, up to a few exceptions, D contains a free pair of symmetric elements provided that (a) it is finite-dimensional and the center has a finite sufficiently large transcendence degree over the prime field, or (b) the center is uncountable, but not algebraically closed in D. Under conditions (a), if the involution...

For a smooth complex projective variety X defined over a number field, we have filtrations on the Chow groups depending of 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...

Gerotranscendence defines a shift in meta-perspective from earlier materialistic and pragmatic concerns, toward more cosmic and transcendent ones in later life. Population-based studies that have empirically examined this concept using Tornstam's gerotranscendence scale, highlight cosmic transcendence as a core component, which includes a sense of belongingness with past and future generations....

We studied the developmental trends of temperament and character in a longitudinal population-based sample of Finnish men and women aged 20-45 years using the Temperament and Character Inventory model of personality. Personality was assessed in 1997, 2001, and 2007 (n = 2,104, 2,095, and 2,056, respectively). Mean-level changes demonstrated qualitatively distinct developmental patterns for char...

for analyzing the issue of coincidence of immanence with transcendence in whitehead’s process philosophy, the present paper attempts at the beginning to show that in this process system, especially in the framework of inclusive and comprehensive categories, entities should be interweave and have organic interrelation; because all the actual entities have reaction against each other. so the prer...

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 ...