A result of Bridson, Howie, Miller and Short states that if $S$ is a subgroup type $FP_{n}(\mathbb{Q})$ the direct product $n$ limit groups over free groups, then virtually groups. Furthermore, they characterise finitely presented residually In this paper these results are generalised to Droms right-angled Artin RAAGs with property all their generated subgroups again RAAGs. addition, we show co...

This paper concerns the question of whether a more direct limit can be used to obtain the limit Hilbert Kunz multiplicity, a possible candidate for a characteristic zero Hilbert-Kunz multiplicity. The main goal is to establish an affirmative answer for one of the main cases for which the limit Hilbert Kunz multiplicity is even known to exist, namely that of graded ideals in the homogeneous coor...

In this study, we first define the concept of inverse and direct system in category of fuzzy modules. We investigate whether or not limit of inverse (direct) system of exact sequences of fuzzy modules is exact. Later, we show that direct system limit of exact sequences of fuzzy modules is exact. Generally, limit of inverse system of exact sequences is not exact. Then we define the notion ← (1) ...

In this short communication, we present a new limit relation that reduces pseudo-Jacobi polynomials directly to Hermite polynomials. The proof of is based upon 2F1-type hypergeometric transformation formulas, which are applicable even and odd separately. This opens the way studying exactly solvable harmonic oscillator models in quantum mechanics terms