Given a λ-ring A and a formally etale morphism f : A→ B of commutative rings, one may ask: What are the possible λ-ring strutures on B such that f is a map of λ-rings? We give the answer: Such a lifted λ-ring structure on B is determined uniquely by a compatible choice of lifts of the Adams operations ψ from A to B for all primes p which satisfy Frobenius congruences. In other words, to extend ...

In the title compound, C(31)H(30)N(2)O(2)S, the pyrrolidine ring adopts a twist conformation while the tetra-hydro-pyridine ring is in a half-chair conformation. The two rings are trans-fused. The pyridine-bound phenyl ring forms dihedral angles of 17.7 (1) and 48.1 (1)°, respectively, with the tosyl and benzyl phenyl rings. The mol-ecular structure is stabilized by an N-H⋯π inter-action involv...

In the title compound, C(14)H(10)FN(3)O, the six- and five-membered rings of the isatin moiety and the six-membered ring of phenyl-hydrazone are nearly planar with r.m.s. deviations of 0.0003, 0.0004 and 0.007 Å, respectively. The dihedral angle between the phenyl ring and the isatin ring system is 6.09 (9)°. The mol-ecular structure is stabilized by a strong intra-molecular N-H⋯O hydrogen bond...

In the title compound, C(15)H(20)ClNO(3), the seven-membered ring adopts a distorted boat-sofa conformation; the methyl-ene C atoms of this ring are coplanar with the benzene ring. Both meth-oxy groups are almost coplanar with the attached benzene ring [C-C-O-C = 6.5 (2) and -13.5 (3)°]. An intra-molecular C-H⋯O hydrogen bond is observed in the mol-ecular structure. In the crystal structure, a ...

Electro-optic modulators lie at the heart of complex integration and high-density electro-optic systems. One representative is thin-film lithium niobate-based microring modulator which has demonstrated advantages compact footprint, low optical loss, high modulation efficiency. However, linewidth extinction ratio ring are fundamentally limited by losses coupling, respectively. To this end, a nov...

In the mol-ecule of the title compound, C(25)H(16)N(4), the pyridine rings are oriented at a dihedral angle of 0.92 (3)°, while the dihedral angle between the benzene ring and the adjacent pyridine ring is 56.51 (3)°. In the crystal structure, inter-molecular N-H⋯N hydrogen bonds link the mol-ecules into centrosymmetric dimers, forming R(2) (2)(16) ring motifs. π-π contacts between the pyridine...

We give some general results on the ring structure of Hochschild cohomology of smash products of algebras with Hopf algebras. We compute this ring structure explicitly for a large class of finite dimensional Hopf algebras of rank one.

In this paper, we define a new algebraic structure of an induced fuzzy k-ideal of a HX ring and some related properties are investigated. The purpose of this study is to implement the fuzzy set theory and ring theory in fuzzy HX k-ideals of a HX ring. We also establish the relation between fuzzy HX ideals and fuzzy HX k-ideals of a HX ring . Characterizations of level subsets of a fuzzy HX k-id...