It is well-known that the theory of algebraically closed fields is not finitely axiomatizable. In this note, we prove that the theory of integrally closed integral domains is also not finitely axiomatizable. All rings in this paper are assumed commutative with identity. Let L be the language of rings, that is, the language whose signature consists of equality, binary function symbols + and ·, a...

We study the massless scalar field on asymptotically flat spacetimes with closed timelike curves (CTC’s), in which all future-directed CTC’s traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. For a class of static geometries of this type, and for smooth initial data with all derivatives in L2 on I−, we prove existence of smooth solutions

This paper is concerned with the completion of proof Bergman centralizer theorem using generic matrices based on our previous quantization (Kanel-Belov et al. in Commun Algebra 46:2123–2129, 2018). Additionally, we establish that algebra characteristic coefficients integrally closed.

manuscripta mathematica manuscript No. Abstract. The core of a projective dimension one module is computed explicitly in terms of Fitting ideals. In particular, our formula recovers previous work by R. Mohan on integrally closed torsionfree modules over a two-dimensional regular local ring.