Let $D$ be a division ring with center $F$, and $G$ subnormal or quasinormal subgroup of $D^*$. We show that if is locally solvable, then contained in $F$.

Assembly of the proto-ring, formed by the essential FtsZ, FtsA and ZipA proteins, and its progression into a divisome, are essential events for Escherichia coli division. ZapC is a cytoplasmic protein that belongs to a group of non-essential components that assist FtsZ during proto-ring assembly. Any overproduction of these proteins leads to faulty FtsZ-rings, resulting in a cell division block...

Correct positioning of the cell division machinery is crucial for genomic stability and cell fate determination. The fission yeast Schizosaccharomyces pombe, like animal cells, divides using an actomyosin ring and is an attractive model to study eukaryotic cytokinesis. In S. pombe, positioning of the actomyosin ring depends on the anillin-related protein Mid1p. Mid1p arrives first at the medial...

Bacterial cell division is driven by the polymerization of GTPase FtsZ into a contractile structure, so-called Z-ring. This essential process involves proteins that modulate dynamics and hence overall Z-ring architecture. Actinobacteria like Streptomyces Mycobacterium lack known key FtsZ-regulators. Here we report identification SepH, conserved actinobacterial protein directly regulates dynamic...

Among the events that accompanied the evolution of chloroplasts from their endosymbiotic ancestors was the host cell recruitment of the prokaryotic cell division protein FtsZ to function in chloroplast division. FtsZ, a structural homologue of tubulin, mediates cell division in bacteria by assembling into a ring at the midcell division site. In higher plants, two nuclear-encoded forms of FtsZ, ...

The essential cytoskeletal protein FtsZ assembles into a ring-like structure at the nascent division site and serves as a scaffold for the assembly of the prokaryotic division machinery. We previously characterized EzrA as an inhibitor of FtsZ assembly in Bacillus subtilis. EzrA interacts directly with FtsZ to prevent aberrant FtsZ assembly and cytokinesis at cell poles. EzrA also concentrates ...

This paper proposes a divider structure that combines a novel self-timed ring structure and a carry-propagation-free division algorithm. The self-timed ring structure enables the divider to compute at a speed comparable to that of previously designed dividers with less silicon area. By exploiting the carry-propagation-free division algorithm, we can achieve even better performance. We designed ...

In the paper we study the endomorphim semigroup of a general quantum polynomial ring, its finite groups of automorphisms and homological properties of this ring as a module over the skew group ring of a finite group of automorphisms. Moreover properties of the division ring of fractions are considered.

The division site in both chloroplasts and bacteria is established by the medial placement of the FtsZ ring, a process that is in part regulated by the evolutionarily conserved components of the Min system. We recently showed that mechanosensitive ion channels influence FtsZ ring assembly in both Arabidopsis thaliana chloroplasts and in Escherichia coli; in chloroplasts they do so through the s...