The ring system of the fungal metabolite (-)-TAN-2483B has been synthesised, for the first time, from d-mannose, utilising a cyclopropanation/ring expansion sequence.

A result of Watanabe and Yoshida says that an unmixed local ring of positive characteristic is regular if and only if its Hilbert-Kunz multiplicity is one. We show that, for fixed p and d, there exist a number ǫ(d, p) > 0 such that any nonregular unmixed ring R its Hilbert-Kunz multiplicity is at least 1+ ǫ(d, p). We also show that local rings with sufficiently small Hilbert-Kunz multiplicity a...

The recent work of Gharib, Rambod, and Shariff @J. Fluid Mech. 360, 121 ~1998!# studied vortex rings formed by starting jets generated using a piston-cylinder mechanism. Their results showed that vortex rings generated from starting jets stop forming and pinch off from the generating jet for sufficiently large values of the piston stroke to diameter ratio (L/D), suggesting a maximization princi...

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

Using simplified model derivatives, the assembly of the macrocyclic rings of madangamines, including the 13- and 14-membered D rings of madangamines C-E, the all-cis-triunsaturated 15-membered D ring of madangamine A, and the (Z,Z)-unsaturated 11-membered E ring common to madangamines A-E, has been studied.

Let A be a ring of dimension d containing an infinite field k, T1,…,Tr variables over and P projective A[T1,…,Tr]-module rank n. Assume one the following conditions holds. 2n≥d+3 is extended from A. 2n≥d+2, affine F‾p-algebra singular locus Spec(A) closed set V(J) with ht J≥d−n+2.

This paper generalizes slightly a result of Kunz [l ] and Nakai [2]. If R>S are commutative rings with identity we introduce a module D*(R/S) defined as the quotient of the module D(R/S) oí S differentials of A by the submodule consisting of elements which are mapped to zero by every homomorphism of D(R/S) having values in a finitely generated A module. The characteristic exponent of a field is...

For a totally positive definite quadratic form over the ring of integers real number field $K$, we show that there are only finitely many extensions $K$ fixed degree which is universal (namely, those have short basis in suitable sense). Along way give general construction rank bounded by $D(\log D)^{d-1}$, where $d$ $\mathbb Q$ and $D$ its discriminant. Furthermore, for any prove (weak) Kitaoka...

Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x), x], [d(y), y]] = 0, for all x, y ∈ I. We prove that if [I, I]I ≠ 0, then d(I)I = 0. 1. Introduction. Let R be a prime ring and d a nonzero derivation of R. Define [x, y] 1 = [x, y] = xy − yx, then an Engel condition is a polynomial [x, y] k = [[x, y] k−1 ,y]