Let K be a field and let A be a finitely generated prime K-algebra. We generalize a result of Smith and Zhang, showing that if A is not PI and does not have a locally nilpotent ideal, then the extended centre of A has transcendence degree at most GKdim(A) − 2 over K. As a consequence, we are able to show that if A is a prime K-algebra of quadratic growth, then either the extended centre is a fi...

For n = 1, the space of R-places of the rational function field R(x1, . . . , xn) is homeomorphic to the real projective line. For n ≥ 2, the structure is much more complicated. We prove that the space of R-places of the rational function field R(x, y) is not metrizable. We explain how the proof generalizes to show that the space of R-places of any finitely generated formally real field extensi...

We prove a pro-p Hom-form of the birational anabelian conjecture for function fields over sub-p-adic fields. Our starting point is the corresponding Theorem of Mochizuki in the case of transcendence degree 1.

Let ξ1, . . . , ξr be complex numbers with K = Q(ξ1, . . . , ξr) having transcendence degree r − 1 over Q. Consider the equation a1x1 + · · ·+ akxk = 1, (1) in which the ai’s are fixed elements of K ×, no proper subsum ai1xi1 + · · ·+ aijxij vanishes, and we seek solutions xi ∈ Γ = ξ1, . . . , ξr . It is well–known that (1) has only finitely many solutions; we present here an elementary proof o...

The purpose of this expository article is to explain diverse new tools that automata theory provides to tackle transcendence problems in function field arithmetic. We collect and explain various useful results scattered in computer science, formal languages, logic literature and explain how they can be fruitfully used in number theory, dealing with transcendence, refined transcendence and class...

BACKGROUND Although successful aging is most often defined by the absence of disease and disability, older adults consistently report aging successfully even in the presence of chronic illness and functional limitations. A more holistic way of looking at old age suggests transcendence may be an important missing criterion for successful aging. AIM Transcendence, a late life developmental proc...

Although we live in a post-metaphysical age, there is a renewed interest in transcendence, especially at the intersection of philosophy, religion, and theology. There are several reasons for this: among others, the important link that the future (eschatology) has with the unknown or that which lies beyond (transcendence). In this article, this relation between eschatology and transcendence is e...

The article presents the understanding of transcendence person in Wojtyła’s phi­losophy. text discusses turn: role experience person; concept transcend­ence relation to other concepts used by Wojtyła; reference truth as basis personal transcendence; integration existence. analyses conducted show that proper sense reveals spiritual dimension his existence being superior material dimension. prese...

We develop an algorithm for computing isomorphisms and automorphisms of algebraic function fields of transcendence degree one in characteristic zero and positive characteristic.

OBJECTIVES Gerotranscendence has been conceptualized as a potential development accompanying normal aging. Gerotranscendence is defined as a shift in metaperspective from a materialistic and pragmatic world view to a more cosmic and transcendent one. In the past decade, population-based studies have tested Tornstam's Gerotranscendence Scale. Its Cosmic Transcendence subscale, in particular, eme...