The title compound, C20H15N3OS, is V-shaped. In the 4-phen-oxy-phenyl group, the two rings are inclined to one another by 74.52 (13)°. These rings are inclined to the triazole ring by 72.20 (15) and 72.30 (15)°, respectively. The phenyl ring is inclined to the triazole ring by 10.85 (12)°. In the crystal, mol-ecules are linked via N-H⋯N hydrogen bonds, forming chains propagating along [010]. Th...

Let k be a number field and letM be a simple k-algebra with center k of rank n, i.e. dimk(M) = n 2. Fix a k-involution x 7→ xτ on M , i.e. (xy)τ = yτxτ as well as (xτ )τ = x and xτ = x when x ∈ k. We will assume that M and τ are defined over the ring of integers O of k. The standard example will be the algebra of n× n matrices Matn(k) and x τ = xt the transposed matrix. For any ringR over k let...

We present a constructive interpretation of some results in [6]. To any integral domain R we associate a distributive lattice V (R) which is a point-free presentation of the space of valuations over the ring R. Our definition, by generators and relations, is similar to Joyal’s definition of the Zariski lattice of a ring R, which is a point-free presentation of the Zariski spectrum of R. The spa...

In this paper, we study congruences for modular forms of half-integral weight on Γ0(4). Suppose that ` ≥ 5 is prime, that K is a number field, and that v is a prime of K above `. Let Ov denote the ring of v-integral elements of K, and suppose that f(z) = ∑∞ n=1 a(n)q n ∈ Ov[[q]] is a cusp form of weight λ + 1/2 on Γ0(4) in Kohnen’s plus space. We prove that if the coefficients of f are supporte...

In this work, we investigate the transfer of some homological properties from a ring $R$ to its amalgamated duplication along some ideal $I$ of $R$ $Rbowtie I$, and then generate new and original families of rings with these properties.

Superconducting thin-film rings smaller than the film penetration depth ~the Pearl length! are considered. The current distribution, magnetic moment, and thermodynamic potential F(H ,N ,v) for a flat, washer-shaped annular ring in a uniform applied field H perpendicular to the film are solved analytically within the London approach for a state with winding number N and a vortex at radius v betw...

Theorem. (Auslander-Buchsbaum-Serre, 1956; see [2] and [24].) Let V be an affine algebraic variety over an algebraically closed field with coordinate ring R. Then the global dimension of R is finite if and only if V is smooth. If this is the case, then gl dimR = dimV . (That the global dimension of R is bounded above by n means that n-fold iteration of the process of taking syzygies of R-module...

with a given q ∈ F×. In particular, in the classical case with F = Q and V = Q, we usually assume that φ is Z-valued on Z and q ∈ Z. The purpose of the present article is to present some new ideas on various arithmetical questions on such an equation. We start with some of our basic symbols and terminology. For a set X we denote by #X or #{X} the number (≤ ∞) of elements of X. For an associativ...

We consider two variants of the task of spreading a swarm of agents uniformly on a ring graph. Ant-like oblivious agents having limited capabilities are considered. The agents are assumed to have little memory, they all execute the same algorithm and no direct communication is allowed between them. Furthermore, the agents do not possess any global information. In particular, the size of the rin...