Conventional techniques for division in the polynomial factor ring F[z]/〈m〉 or the integer ring Zn use a combination of inversion and multiplication. We present a new algorithm that computes the division directly and therefore eliminates the multiplication step. The algorithm requires 2 degree(m) (resp. 2 log 2 n) steps, each of which uses only shift and multiply-subtract operations.

In plants, chloroplast division is an integral part of development, and these vital organelles arise by binary fission from pre-existing cytosolic plastids. Chloroplasts arose by endosymbiosis and although they have retained elements of the bacterial cell division machinery to execute plastid division, they have evolved to require two functionally distinct forms of the FtsZ protein and have los...

Jacobson's generalization [5, Theorem 8] of Wedderburn's theorem [8] states that an algebraic division algebra over a finite field is commutative. These algebras have the property that some power2 of each element lies in the center. Kaplansky observed in [7] that any division ring, or, more generally, any semisimple ring, in which some power of each element lies in the center is commutative. Ka...

What is the contractile ring? During cell division, the contractile ring generates the constricting force to separate one cell into two cells. Formed during cytokinesis, the last step of cell division, the contractile ring is composed of filamentous actin (F-actin) and the motor protein myosin-2, along with additional structural and regulatory proteins. The contractile ring forms under the surf...