The splitting of the Goldie (or singular) torsion theory has been extensively studied. Here we determine an appropriate dual Goldie torsion theory, discuss its splitting and answer in the negative a question proposed by Özcan and Harmancı as to whether the splitting of the dual Goldie torsion theory implies the ring to be quasi-Frobenius.

A torsion theory is called differential (higher differential) if a derivation (higher derivation) can be extended from any module to the module of quotients corresponding to the torsion theory. We study conditions equivalent to higher differentiability of a torsion theory. It is known that the Lambek, Goldie and any perfect torsion theories are differential. We show that these classes of torsio...

Abstract The theory of generalized Nijenhuis torsions, which extends the classical notions due to and Haantjes, offers new tools for study normal forms operator fields. We prove a general result ensuring that, given family commuting fields whose torsion level m vanishes, there exists local chart where all operators can be simultaneously block-diagonalized. also introduce notion Haantjes algebra...

We compare the description of M-theory form fields via cohomotopy versus that integral cohomology. The conditions for lifting latter to former are identified using obstruction theory in Postnikov towers, where torsion plays a central role. A subset these is shown correspond compatibly existing consistency conditions, while rest new and point further requirements M-theory. Bringing geometry lead...

We obtain the solution that corresponds to a screwed superconducting cosmic string (SSCS) in the framework of a general scalar-tensor theory including torsion. We investigate the metric of the SSCS in Brans-Dicke theory with torsion and analyze the case without torsion. We show that in the case with torsion the space-time background presents other properties different from that in which torsion...

The Floer homology can be trivial in many variants of the Floer theory; it is therefore interesting to consider more refined invariants of the Floer complex. We consider one such instance—the Reidemeister torsion τF of the Floer complex of (possibly non-hamiltonian) symplectomorphisms. τF turns out not to be invariant under hamiltonian isotopies, but we introduce a “correction term”—the Floerth...

We point out that a background torsion field will produce an effective potential to the K and K̄ with opposite signs. This allows us to constrain the background torsion field from the KL and KS mass difference, CPT violating K ◦ and K̄ mass difference and the CP violating quantities ǫ and η+−. The most stringent bound on the cosmological background torsion 〈T 0〉 < 10−25 GeV comes from the direct ...

We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology their asymptotic boundaries. The underlying geometric structures are shown to be equivalent known characterizations gauge group in via Mordell--Weil torsion string junctions. further study dimensional reductions 11d Chern--Simons term presence torsional boundary $G_4$-fluxes, whi...

Orientifolds of the type IIB superstring that descend from F theory and M theory orbifolds are studied perturbatively. One finds strong evidence that a previously ignored twisted open string is required in these models. An attempt is made to interpret the J type torsion in F theory where one finds a realization of Gimon and Johnson’s models which does not require these twisted strings. S-dualit...

The answer is yes, if ... This note attempts to give amplification to the above statement, while at the same time arriving at a reasonable description of this lattice. The main theorem of the paper is no doubt the assertion that the lattice of torsion classes of lattice-ordered groups is completely distributive. The proof of this theorem depends on the notion of a value selector, and should not...