Sterically Constrained Bicyclic Phosphines: A Class of Fascinating Compounds Suitable for Application in Small Molecule Activation and Coordination Chemistry

Bicyclic phosphines with two annulated, electronically unsaturated five-membered heterocycles are available through facile routes. In most cases, their phosphorus atoms are bound to heteroatoms such as oxygen or nitrogen (PN₃ or PN₂O), whereas homoleptic coordination by three sp²-hybridized carbon atoms has been reported only recently. Steric strain causes unique reactivity. Oxidative addition of halogens, N−H or O−H bonds have afforded phosphoranes as valuable materials for secondary processes. Ring opening was identified as an important step for the understanding of these reactions and has been observed experimentally with a diphosphorus-based ring system. A PH₂ derivative has been considered as a model system for small molecule activation, and hydrogen transfer to a diazo compound was observed experimentally. Several of these phosphines are excellent ligands for the coordination of transition-metal atoms. The very bulky PC₃ compound has a basicity similar to that of PPh₃ and may allow the synthesis of complexes with unusually low coordination numbers at the metal atoms. These phosphines found recently renewed interest as promising reagents in various secondary transformations such as the activation of σ-bonds or in coordination chemistry.     

Aryl vinyl cyclopropane Cope rearrangements

While the divinyl cyclopropane Cope rearrangement is well-known, and has been broadly applied in synthesis, examples of the aryl vinyl cyclopropane Cope rearrangement are less common and generally limited in scope or reaction yield. The aryl vinyl cyclopropane Cope rearrangement gives access to the benzocycloheptene scaffold, which is present in a variety of naturally occurring and medicinally relevant products. Herein we report a method to obtain either of two regioisomeric benzocycloheptene products via an aryl vinyl cyclopropane Cope rearrangement, featuring additive-controlled regioselectivity. Mechanistic studies indicate a dynamic equilibration of cyclopropane stereoisomers, followed by rearrangement of the cis diastereomer.     

Rings with 2-UJ property

Abstract

Rings in which the square of each unit is a sum of an idempotent and an element from the Jacobson radical are said to be 2-UJ. Properties of 2-UJ rings are discussed, and the 2-UJ property is applied to characterize some known notions of rings.     

Group inverse and core inverse in Banach and C*-algebras

Abstract

In this paper, we have focused our study on the acute perturbation of the group inverse for the elements of Banach algebra with respect to the spectral radius. We also give perturbation analysis for the core inverse in C*- algebra. The perturbation bounds for the core inverse under some conditions are presented. Additionally, this paper extends the results obtained in [11, 14].     

On idempotents of a class of commutative rings

Abstract

In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are determined. Several examples are included illustrating the main results.     

Rings whose singular ideals are nil

Abstract

It is well known that when a ring R satisfies ACC on right annihilators of elements, then the right singular ideal of R is nil, in this case, we say R is right nil-singular. Many classes of rings whose singular ideals are nil, but do not satisfy the ACC on right annihilators, are presented and the behavior of them is investigated with respect to various constructions, in particular skew polynomial rings and triangular matrix rings. The class of right nil-singular rings contains π-regular rings and is closed under direct sums. Examples are provided to explain and delimit our results.