Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ (A) the Auslander–Reiten quiver of A. We show that A is representation-finite if and only if Γ (A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander–Reiten translation. Let K denote a fixed algebraically closed fie...

Let M be a module over an associative ring R and σ[M ] the category of M -subgenerated modules. Generalizing the notion of a projective generator in σ[M ], a module P ∈ σ[M ] is called tilting in σ[M ] if (i) P is projective in the category of P -generated modules, (ii) every P -generated module is P presented, and (iii) σ[P ] = σ[M ]. We call P self-tilting if it is tilting in σ[P ]. Examples ...

A torsion pendulum without a torsion wire has been designed and realized, in order to measure very weak forces. The arm of this torsion pendulum ~5.40 g, 1.32310 kg m of inertia! is electrostatically suspended. Its 6 degrees of freedom are controlled thanks to electrostatic forces, and capacitive position sensing with a noise spectral density between 10 and 10 m/AHz. The torque noise spectral d...

We present a quick approach to computing the K-theory of category locally compact modules over any order in semisimple ℚ-algebra. obtain by first quotienting out and subsequently vector modules. Our proof exploits fact that pair (vector plus modules, discrete modules) becomes torsion theory after we quotient finite Treating these quotients as exact categories is possible due recent localization...

All rings are commutative with 1 6= 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a, b ∈ R and m ∈M and abm ∈ N , then am ∈M -rad(N) or bm ∈M -rad(N) or ...

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...