Let Fq be a finite field of characteristic p, K a field containing it, and R = K[X1, . . . , Xn] a polynomial ring in n variables. The general linear group GLn(Fq) has natural action on R by degree preserving ring automorphisms. L. E. Dickson showed that the subring of elements which are fixed by this group action is a polynomial ring, [Di], though for an arbitrary subgroupG of GLn(Fq), the str...

We study the ring Γ of all functions N → K, endowed with the usual convolution product. Γ, which we call the ring of number-theoretic functions, is an inverse limit of the “truncations” Γn = { f ∈ Γ ∀m > n : f(m) = 0 } . Each Γn is a zero-dimensional, finitely generated K-algebra, which may be expressed as the quotient of a finitely generated polynomial ring with a stable (after reversing the o...

In the title compound, C25H23FN2O4S, the fused piperidine ring of the octa-hydro-indolizine ring system adopts a chair conformation and the five-membered ring has a twisted conformation on the N-C(spiro) bond. The mean planes of the benzo-thio-phene and indoline ring systems are inclined to the mean plane of the pyrrolidine ring by 83.1 (1) and 84.9 (1)°, respectively, and to each other by 29.3...

In the asymmetric unit of the title compound {systematic name: 3-chloro-N-[3-chloro-5-(tri-fluoro-meth-yl)pyridin-2-yl]-2,6-di-nitro-4-(tri-fluoro-methyl)-aniline}, C13H4Cl2F6N4O4, which is the fungicide fluazinam, the dihedral angle between the pyridine and benzene ring planes is 42.20 (4)°. In the crystal, pairs of N-H⋯F hydrogen bonds link the mol-ecules into inversion dimers which are linke...

Let p be a prime number. A finite Galois extension N/F of a number field F with group G has a normal p-integral basis (p-NIB for short) when O′ N is free of rank one over the group ring O′ F [G]. Here, O′ F = OF [1/p] is the ring of p-integers of F . Let m = p be a power of p and N/F a cyclic extension of degree m. When ζm ∈ F×, we give a necessary and sufficient condition for N/F to have a p-N...

The title compound, C(20)H(14)F(4)N(4), is a flexible bis-pyridine-type ligand with an extended fluorinated spacer group between the two pyridyl functions. The centroid of the central aromatic ring is situated on a crystallographic center of inversion. The dihedral angle between the pyridine ring and the central benzene ring is 63.85 (9)°. The crystal structure exhibits inter-molecular C-H⋯F hy...

In the title compound, C(13)H(10)F(3)N(3)O(5), a derivative of andrographolide, the five-membered ring adopts an envelope conformation, while the non-planar six-membered ring has a chair conformation. An intra-molecular C-H⋯F hydrogen bond results in the formation of a non-planar six-membered ring adopting a twisted conformation. In the crystal structure, inter-molecular C-H⋯O hydrogen bonds li...

Let K be a number field and set R = OK , the ring of integers in K. We determine all polynomials f ∈ R[X] and all α ∈ R for which the grand orbit {β ∈ K : f(β) = f(α) for some n,m ≥ 0} contains infinitely many elements of R which are not in the forward orbit {f(α) : n ≥ 0}.

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

In the title compound, C(17)H(15)NO(2)S(2), the 3H-benzo[f]chromene ring system is distinctly twisted; the dihedral angle between the pyran ring and its opposite benzene ring is 9.11 (8)°. The N,N-dimethyl-carbamodithio-ate residue lies almost perpendicular to the pyran ring [dihedral angle = 85.15 (7)°]. In the crystal, weak C-H⋯O hydrogen bonds link the mol-ecules into C(10) chains propagatin...