Russian ruble Russian ruble The Russian ruble or rouble ( "rublʹ", plural: "rubli"; sign: ₽, руб; code: RUB) is the currency of the Russian Federation, the two partially recognised republics of Abkhazia and South Ossetia and the two unrecognised republics of Donetsk and Luhansk. The ruble is subdivided into 100 "kopeks" (sometimes written as "kopecks" or "copecks"; "kopeyka", plural: "kopeyki"). The ruble was the currency of the Russian Empire and of the Soviet Union (as the Soviet ruble). However, today only Russia, Belarus and Transnistria use currencies with the same name. The ruble was the world's first decimal currency: it was decimalised
Divided power structure Divided power structure In mathematics, specifically commutative algebra, a divided power structure is a way of making expressions of the form formula_1 meaningful even when it is not possible to actually divide by formula_2. Let "A" be a commutative ring with an ideal "I". A divided power structure (or PD-structure, after the French "puissances divisées") on "I" is a collection of maps formula_3 for "n" = 0, 1, 2, ... such that: For convenience of notation, formula_18 is often written as formula_19 when it is clear what divided power structure is meant. The term "divided power ideal" refers to an