Let A be an integral domain with field of fractions K. We investigate the structure of the overrings B ⊆ K of A that are wellcentered on A in the sense that each principal ideal of B is generated by an element of A. We consider the relation of well-centeredness to the properties of flatness, localization and sublocalization for B over A. If B = A[b] is a simple extension of A, we prove that B i...

Abstract: We propose a reduced constrained Hamiltonian formalism for the exactly soluble B ∧ F theory of flat connections and closed two-forms over manifolds with topology Σ× (0, 1). The reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group π1(Σ ), and elements of the second cohomology group of Σ with value in the Lie alge...

Let R be a Dedekind domain, G an affine flat R-group scheme, and B a flat R-algebra on which G acts. Let A → BG be an R-algebra map. Assume that A is Noetherian. We show that if the induced map K ⊗ A → (K ⊗ B)K⊗G is an isomorphism for any algebraically closed field K which is an R-algebra, then S ⊗A→ (S ⊗B)S⊗G is an isomorphism for any R-algebra S.

Properties of (most general) non-commutative torsors or A-B torsors are analysed. Starting with pre-torsors it is shown that they are equivalent to a certain class of Galois extensions of algebras by corings. It is then concluded that every faithfully flat unital pre-torsor admits a (left and right) flat (bimodule) connection. It is shown that a class of faithfully flat pre-torsors induces equi...

We show (a) that any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the Euclidean metric is flat; (b) that any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the...

In this paper‎, ‎we study the class of rings in which every $P$-flat‎ ‎ideal is flat and which will be called $PFF$-rings‎. ‎In particular‎, ‎Von Neumann regular rings‎, ‎hereditary rings‎, ‎semi-hereditary ring‎, ‎PID and arithmetical rings are examples of $PFF$-rings‎. ‎In the context domain‎, ‎this notion coincide with‎ ‎Pr"{u}fer domain‎. ‎We provide necessary and sufficient conditions for‎...

in 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $a_{s}$ over a monoid $s$ that can be described by means of when the functor $a_{s} otimes -$ preserves pullbacks. in this paper, we extend these results to$s$-posets and present equivalent descriptions of weakly kernel po...

Kleinewillinghöfer classified Laguerre planes with respect to central automorphisms. Polster and Steinke investigated flat Laguerre planes and their so-called Kleinewillinghöfer types, that is, the Kleinewillinghöfer types with respect to the full automorphism group. For some of these types the existence question remained open. We provide strong necessary existence conditions for flat Laguerre ...

Magnetic field effects on single-particle energy bands (Hofstadter butterfly), Hall conductance, flat-band ferromagnetism, and magnetoresistance of twodimensional Kagome lattices are studied. The flat-band ferromagnetism is shown to be broken as the flat-band has finite dispersion in the magnetic field. A metal-insulator transition induced by the magnetic field (giant negative magnetoresistance...