Given two rings R ⊆ S, S is said to be a minimal ring extension of R if R is a maximal subring of S. In this article, we study minimal extensions of an arbitrary ring R, with particular focus on those possessing nonzero ideals that intersect R trivially. We will also classify the minimal ring extensions of prime rings, generalizing results of Dobbs, Dobbs & Shapiro, and Ferrand & Olivier on com...

The mol-ecule of the title compound, C(22)H(18)N(4)O(2)S(2), lies across a crystallographic inversion centre. The central benzene ring forms dihedral angles of 29.39 (9) and 79.11 (12)°, respectively, with the thio-urea unit and the terminal phenyl ring. Intra-molecular N-H⋯O hydrogen bonds generate two S(6) ring motifs. In the crystal, mol-ecules are linked into chains along [10] by inter-mole...

In the title compound, C34H28N2S2, the central imidazole ring (r.m.s. deviation = 0.0015 Å) forms dihedral angles of 55.7 (3), 17.94 (11) and 86.27 (11)°, respectively, with the mean planes of the attached thienyl and two phenyl substituents. The thienyl ring shows ring-flip disorder [occupancy ratio = 0.647 (2):0.353 (2)]. The chiral centre maintains the S configuration of the l-phenyl-alanino...

In the title compound, C(14)H(20)N(2)O(3)S, the cyclo-hexyl ring adopts a chair conformation: the four coplanar C atoms of this ring make a dihedral angle of 64.8 (2)° with the benzene ring. In the mol-ecule, an intra-molecular C-H⋯O contact generates an S(6) ring motif. In the crystal structure, mol-ecules are linked via inter-molecular N-H⋯O hydrogen bonds into two-dimensional layers propagat...

The title mol-ecule, C(30)H(37)N(5)S, displays a chair-shaped piperazine ring, as well as an approximately planar triazole ring [maximum deviation = 0.002 (2) Å] whose phenyl substituent is nearly perpendicular to the mean plane of the five-membered ring [dihedral angle = 80.4 (1)°]. The substit-uents on the piperazine ring occupy equatorial sites. Weak inter-molecular C-H⋯S hydrogen bonding is...

In this note we give examples of a ring that has no maximal ideals. Recall that, by a Zorn’s lemma argument, a ring with identity has a maximal ideal. Therefore, we need to produce examples of rings without identity. To help motivate our examples, let S be a ring without identity. We may embed S in a ring R with identity so that S is an ideal of R. Notably, set R = Z⊕S, as groups, and where mul...

In the title compound, C(11)H(9)F(2)N(5)OS, the pyrazole ring forms a dihedral angle of 16.42 (6)° with the benzene ring. Intra-molecular N-H⋯O hydrogen bonds generate two S(6) ring motifs. In the crystal, an R(2) (2)(8) ring motif is formed by a pair of inter-molecular N-H⋯S hydrogen bonds. Inter-molecular C-H⋯F hydrogen bonds further link the mol-ecules into a three-dimensional network.

In the asymmetric unit of the title compound, C(16)H(11)FO(5)S, the 2H-chromene ring is essentially planar, with a maximum deviation of 0.040 (2) Å. The dihedral angle between the 2H-chromene ring and the 4-fluoro-phenyl ring is 2.17 (8)°. One of the sulfonamide O atoms is approximately coplanar with the benzene ring [C-C-S-O torsion angle = 166.00 (14)°], whereas the other O atom lies well bel...

Using the solitonic solution-generating technique we rederived the one-rotational five-dimensional black ring solution found by Emparan and Reall. The seed solution is not the Minkowski metric, which is the seed of S-rotating black ring. The obtained solution has more parameters than the Emparan and Reall’s S-rotating black ring. We found the conditions of parameters to reduce the solution to t...