Center (ring theory)In algebra, the center of a ring R is the subring consisting of the elements x such that xy = yx for all elements y in R. It is a commutative ring and is denoted as ; "Z" stands for the German word Zentrum, meaning "center". If R is a ring, then R is an associative algebra over its center. Conversely, if R is an associative algebra over a commutative subring S, then S is a subring of the center of R, and if S happens to be the center of R, then the algebra R is called a central algebra.
CyclopentadieneCyclopentadiene is an organic compound with the formula C5H6. It is often abbreviated CpH because the cyclopentadienyl anion is abbreviated Cp−. This colorless liquid has a strong and unpleasant odor. At room temperature, this cyclic diene dimerizes over the course of hours to give dicyclopentadiene via a Diels–Alder reaction. This dimer can be restored by heating to give the monomer. The compound is mainly used for the production of cyclopentene and its derivatives.
AbacusThe abacus (: abaci or abacuses), also called a counting frame, is a hand-operated calculating tool of unknown origin used since ancient times in the ancient Near East, Europe, China, and Russia, millennia before the adoption of the Hindu-Arabic numeral system. The abacus consists of multiple columns of slidable beads (or similar objects). In their earliest designs, the columns of beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation.
