Bazzoni’s Conjecture states that the Prüfer domain R has finite character if and only if R has the property that an ideal of R is finitely generated if and only if it is locally principal. In [4] the authors use the language and results from the theory of lattice-ordered groups to show that the conjecture is true. In this article we supply a purely ring theoretic proof. 1. Bazzoni’s Conjecture ...

We use Dirac matrix representations of the Clifford algebra to build fracton models on lattice and their effective Chern-Simons-like theory. As an example we fractons in odd $D$ spatial dimensions $(D+1)$ The model possesses anti-symmetric $K$ resembling that hierarchical quantum Hall states. gauge charges are conserved sub-dimensional manifolds which ensures fractonic behavior. construction ex...

A brief review of a Conformal Gravity and U(4)×U(4) Yang-Mills Unification model in four dimensions from a Clifford Gauge Field Theory in C-spaces (Clifford spaces) is presented. It based on the (complex) Clifford Cl(4, C) algebra underlying a complexified four dimensional spacetime (8 real dimensions). The 16 fermions of each generation can be arranged into the 16 entries of a 4 × 4 matrix ass...

The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not only of points, but also of 1-loops, 2-loops, etc.. They are associated with multivectors which are the wedge product of the basis vectors, the generators of Cl...

We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension—the so called Clifford space (C-space), a manifold of points, lines, areas, etc..; physical quantities are Clifford algebra valued objects , called polyvectors. This provides a natural framework for description of super-symmetry, since spinors are just left or right ...