A group of 24 bronze finger-rings threaded onto a wire bracelet was unearthed in 2018 at the Roman vicus at Wareswald (the “Forbidden Forest”) in Gallia Belgica. The find is analyzed here alongside evidence for the use, sale, and production of Roman rings. The find represents the work of a local craftsman, active in the first quarter of the 4th c. CE. While the rings were made in a small rural town, they closely imitate expensive global ring forms. The function and meaning of the very common class of trinket rings to which the Wareswald rings belong are considered, along with how these rings were used to make statements about identity, including local and regional affiliations, literacy, marital status, or other social connections. It is suggested that the popularity of many trinket rings lay in their ability to provide a sense of participation in upper-class fashion at a very low price.

Given an action ${\varphi }$ of inverse semigroup S on a ring A (with domain of ${\varphi }(s)$ denoted by $D_{s^*}$ ), we show that if the ideals $D_e$ , with e an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$ can be realized as the convolution algebra of an ample groupoid with coefficients in a sheaf of (unital) rings. Conversely, we show that the convolution algebra of an ample groupoid with coefficients in a sheaf of rings is isomorphic to a skew inverse semigroup ring of this sort. We recover known results in the literature for Steinberg algebras over a field as special cases.

The purpose of this note is to prove the following. Suppose $\mathfrak{R}$ is a semiprime unity ring having an idempotent element $e$ ($e\neq 0,~e\neq 1$) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathfrak{R}$ is a generalized derivation.

In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that network. Subspaces defined by equalities of coordinates which are flow-invariant for any coupled cell system consistent with a network structure are called the network synchrony subspaces. Moreover, for every synchrony subspace, each network admissible system restricted to that subspace is a dynamical system consistent with a smaller network called a quotient network. We characterize networks such that: the network is a subnetwork of its fundamental network, and the network is a fundamental network. Moreover, we prove that the fundamental network construction preserves the quotient relation and it transforms the subnetwork relation into the quotient relation. The size of cycles in a network and the distance of a cell to a cycle are two important properties concerning the description of the network architecture. In this paper, we relate these two architectural properties in a network and its fundamental network.

Let ${\mathcal{A}}$ be a unital ring with involution. Assume that ${\mathcal{A}}$ contains a nontrivial symmetric idempotent and ${\it\phi}:{\mathcal{A}}\rightarrow {\mathcal{A}}$ is a nonlinear surjective map. We prove that if ${\it\phi}$ preserves strong skew commutativity, then ${\it\phi}(A)=ZA+f(A)$ for all $A\in {\mathcal{A}}$, where $Z\in {\mathcal{Z}}_{s}({\mathcal{A}})$ satisfies $Z^{2}=I$ and $f$ is a map from ${\mathcal{A}}$ into ${\mathcal{Z}}_{s}({\mathcal{A}})$. Related results concerning nonlinear strong skew commutativity preserving maps on von Neumann algebras are given.

Interstellar radar is a potential intermediate step between passive observation of exoplanets and interstellar exploratory missions. Compared with passive observation, it has the traditional advantages of radar astronomy. It can measure surface characteristics, determine spin rates and axes, provide extremely accurate ranges, construct maps of planets, distinguish liquid from solid surfaces, find rings and moons, and penetrate clouds. It can do this even for planets close to the parent star. Compared with interstellar travel or probes, it also offers significant advantages. The technology required to build such a radar already exists, radar can return results within a human lifetime, and a single facility can investigate thousands of planetary systems. The cost, although too high for current implementation, is within the reach of Earth's economy.

Motivated by mathematical aspects of origami, Erik Demaine asked which points in the plane can be constructed by using lines whose angles are multiples of $\pi /n$ for some fixed $n$. This has been answered for some specific small values of $n$ including $n=3,4,5,6,8,10,12,24$. We answer this question for arbitrary $n$. The set of points is a subring of the complex plane $\mathbf {C}$, lying inside the cyclotomic field of $n$th roots of unity; the precise description of the ring depends on whether $n$is prime or composite. The techniques apply in more general situations, for example, infinite sets of angles, or more general constructions of subsets of the plane.

Topologically modeled amorphized silica structures have been refined using a molecular dynamics simulation technique. Several metastable structures with substantially different medium-range connectivities, as characterized by primitive ring statistics, were obtained. Whereas the total correlation function is insensitive to these differences, the first sharp diffraction peak derived from energy-filtered electron diffraction shows a promising correlation to medium-range structure.