Let R be a local ring of bounded module type. It is shown that R is an almost maximal valuation ring if there exists a non-maximal prime ideal J such that R/J is an almost maximal valuation domain. We deduce from this that R is almost maximal if one of the following conditions is satisfied: R is a Q-algebra of Krull dimension ≤ 1 or the maximal ideal of R is the union of all non-maximal prime i...

Given any irreducible Coxeter group C of hyperbolic type with nonlinear diagram and rank at least 4, whose maximal parabolic subgroups are finite, we construct an infinite family locally spherical regular hypertopes is the same as that C.

Let S be a smooth projective surface over the field of complex numbers C. Fix a closed point s ∈ S and a pair of positive integers r, d. By results of Grothendieck (cf. [6], [11]) there exists a projective scheme Quot [s] (r, d) parametrizing all quotient sheaves O ⊕r S → A of length d supported at s. We consider this scheme with its reduced scheme structure and call it the punctual Quot scheme...