1.1 By R we denote an integral domain; then R[[x]] is the ring of formal power series over R in the variables x = (x1, . . . , xn). We write a series f(x) ∈ R[[x]] as f(x) = ∑ ai1···inx i1 1 · · ·xin n = ∑ aνx ν where ν = (ν1, . . . , νn) is a multi-index and x = x1 1 · · ·xνn n . In the sequel R is usually the finite field Fp of p elements or the ring of p-adic integers Zp. One says that f(x) ...

In the title compound, C(23)H(20)F(3)N(5)O, the piperazine ring adopts a chair conformation. The quinoline ring makes dihedral angles of 56.61 (11), 49.94 (12) and 42.58 (14)° with the piperazine ring, the 1,3,4-oxadiazole ring and the benzene ring, respectively. An intra-molecular C-H⋯O hydrogen bond generates an S(7) ring motif. In the crystal, mol-ecules are linked into infinite chains along...

In the title compound, C(20)H(15)F(6)N(3)O(2), the quinoline ring system is almost coplanar with the benzene ring; the dihedral angle between the two planes is 2.31 (8)°. The crystal structure displays an inter-molecular C-H⋯F hydrogen bond. In addition, a weak π-π inter-action is observed between the unfused benzene ring and the benzene ring of quinoline, with a centroid-centroid distance of 3...

Let N be a near ring. An additive mapping f : N → N is said to be a right generalized (resp., left generalized) derivation with associated derivation d onN if f(xy) = f(x)y + xd(y) (resp., f(xy) = d(x)y + xf(y)) for all x, y ∈ N. A mapping f : N → N is said to be a generalized derivation with associated derivation d onN iff is both a right generalized and a left generalized derivation with asso...

We call a ring R generalized uniquely clean (or GUC for short) if every not invertible element in is clean. Let be ring. It shown that and only it local or Thus the generalization of Some basic properties rings are proved.

Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.

Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized telescoping solution, proves algebraic independence of certain types of sums. Combining this fact with summation-theory shows transcendence of whole classes of sums. Parameterized telescoping Given f1(k), ....

We reprove Lazard’s result that every commutative n-bud is extendible to an n+ 1 bud, from an obstruction theoretic point of view. We locate the obstruction to extending an arbitrary n-bud in a certain cohomology group, and classify isomorphism classes of n-bud extensions for low degrees. 1 Lubin-Tate cohomology Definition 1. Let R be a commutative, unital ring and F a formal group law on R (as...

Abstract Let D be a finite-dimensional division algebra over its center and R = [ t ; ? , ? ] skew polynomial ring. Under certain assumptions on the ring of central quotients ( ) { f / g | ? ], C ])} is simple with reduced norm N . We calculate for some polynomials investigate when how reducibility reflects

Multidimensional continued fraction algorithms associated with GL n (Z K), where Z k is the ring of integers of an imaginary quadratic field K, are introduced and applied to find systems of fundamental units in families of totally complex algebraic number fields of degrees four, six, and eight. 1. Introduction. Let F be an algebraic number field of degree n. There exist exactly n field embeddin...