CARL FAITH All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective . SISI rings include Noetherian rings, Morita rings, and almost maximal valuation rings ([Vil) . In [F3] we raised the question of whether a polynomial ring R[-1 over a SISI ring R is again SISI . In this paper we show this is not...

In the unsymmetrical title vanadyl complex, [V(C9H9NO2)(C7H5O2)O], one of the ligands (2-formyl-phenol) is disordered over two sets of sites, with an occupancy ratio of 0.55 (2):0.45 (2). The metal atom is hexa-coordinated, with a distorted octa-hedral geometry. The vanadyl O atom (which subtends the shortest V-O bond) occupies one of the apical positions and the remaining axial bond (the longe...

In this paper we introduce the notion of unit-regular ideals for unital rings, which is a natural generalization of unit-regular rings. It is shown that every square matrix over unit-regular ideals admits a diagonal reduction. We also prove that a regular ideal of a unital ring is unit-regular if and only if pseudo-similarity via the ideal is similarity. Let I be an ideal of a unital ring R. We...

The title compound, C42H48O6, was obtained via formyl-ation of 25,26,27,28-tetra-propoxycalix[4]arene with dichloro-methyl methyl ether and tin tetra-chloride. It adopts a pinched cone conformation, which leads to an open cavity. The two opposite aromatic rings bearing formyl groups are almost parallel, making a dihedral angle of 29.1 (2)°. The other pair of opposite rings are close to being pe...

1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Definition of the Witt Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Proof of the Existence of the Witt Rings . . . . . . . . ....

The title compound, C(14)H(16), is built up from three five-membered rings. Two of the five-membered rings display an envelope conformation and the third one is almost planar (r.m.s. deviation = 0.014 Å).

If for any maximal right ideal P of B and a ∈ N(B) ,aB/ aP is almost N-injective, then ring said to be generalized N-injective. In this article, we present some significant findings that are known N-injective rings demonstrate they hold rings. At the same time, study case in which every S.S.Right B-module