We give an explicit account of an argument appearing in Kishimoto's paper. Nothing in this exposition is new. This argument is used in "Actions of tensor categories on Kirchberg algebras", arXiv:2405.18429 (see Lemma 2.4 therein). 

This is an extended abstract of a talk at "Workshop on Operator Theory and Operator Algebras" in November 2023. It contains a primitive version of the proof of (5)⇒(1) in Theorem A from "Semiprime ideals in C*-algebras", arXiv:2311.17480, from which it follows that every (possibly not norm-closed) prime ideal in a C*-algebra is self-adjoint. 

We consider the coordination sequences of molecular solids or lattices with fixed generating sets. Perhaps unintuitively, it turns out that sometimes coordination sequences of molecular solids are not quasi-polynomial, as explicitly calculated for copper(II) oxide. Thanks to the result of Conway-Sloane, we also observe that for a root system Φ all of whose roots have the same length, the coordination sequence of the root lattice of Φ coincides with the difference polynomial of the Ehrhart polynomial of the convex hull of Φ if and only if Φ contains at most one summand of E_7 and E_8 in total.