Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In additio...

There is an Mayer-Vietoris exact sequence 0 → Vn → PicZCpn → Cl Q(ζn−1) × Pic ZCpn−1 → 0 involving the Picard group of the integer group ring ZCpn where Cpn is the cyclic group of order p and ζn−1 is a primitive p -th root of unity. The group Vn splits as Vn ∼= V + n ⊕ V − n and V − n is explicitly known. V + n is a quotient of an in some sense simpler group Vn. In 1977 Kervaire and Murthy conj...

Spontaneous A-V nodal rhythm was observed in 23 isolated, perfused rabbit hearts during electrophysiologic studies of A-V transmission. In 19 of the 23, the earliest point of activation was determined by recording transmembrane potentials from numerous A-V junctional fibers. Most commonly (15 hearts), the earliest depolarization was found in a specific area of the A-V node near the point where ...

Michaelis-Menten parameters for hydrolysis of seven aryl N-acetyl alpha-D-neuraminides by Vibrio cholerae neuraminidase at pH 5.0 correlate well with the leaving-group pKa (delta pK 3.0; beta 1g (V/K) = -0.73, r = -0.93; beta 1g (V) = -0.25; r = -0.95). The beta-deuterium kinetic-isotope effect, beta D2(V), for the p-nitrophenyl glycoside is the same at the optimum pH of 5.0 (1.059 +/- 0.010) a...

Let V be a finite-dimensional representation of a finite group G of order n over a field k. Then by a classical theorem of Hermann Weyl [5] on polarizations one obtains a nice generating set for the invariant ring (SymV ) consisting of er(f), r = 1, 2, . . . , n, f ∈ V ∗ where er(f) denotes the r-th elementary symmetric polynomial in σ.f, σ ∈ G. Also, for any point x ∈ P(V ) there is a G-invari...

In [1] Briançon and Skoda proved, using analytic methods, that if I is an ideal in the convergent power series ring C{x1, . . . , xn} then In, the integral closure of I, is contained in I. Extensive work has been done in the direction of proving “Briançon-Skoda type theorems”, that is, statements about I t being contained in (I t−k)#, where k is a constant independent of t, and # is a closure o...