Small orthomodular partial algebras

Orthomodular partial algebras (OMAs) can be seen as the algebraic representation of orthomodular posets. We use Greechie diagrams for the graphical representation of OMAs and investigate characterizations for the strong embeddability of a given OMA into a Boolean OMA. We present a complete list of the Greechie diagrams of OMAs up to 24 elements, and we show that there exists an infinite OMA that is generated by 4 elements.     

Simultaneous Induction of Axial and Planar Chirality in Arene–Chromium Complexes by Molybdenum‐Catalyzed Enantioselective Ring‐Closing Metathesis

The molybdenum‐catalyzed asymmetric ring‐closing metathesis of the various C_s‐symmetric (π‐arene)chromium substrates provides the corresponding bridged planar‐chiral (π‐arene)chromium complexes in excellent yields with up to >99 % ee. With a bulky and unsymmetrical substituent, such as N‐indolyl or 1‐naphthyl, at the 2‐positions of the η⁶‐1,3‐diisopropenylbenzene ligands, both biaryl‐based axial chirality and π‐arene‐based planar chirality are simultaneously induced in the products. The axial chirality is retained even after the removal of the dicarbonylchromium fragment, and the chiral biaryl/heterobiaryl compounds are obtained with complete retention of the enantiopurity.