Rational mnemofunctions on $\mathbb{R}$

The subspace of rational distributions was considered it this paper. Distribution is called rational if it has analytical representation $f=(f^{+},f^{-})$ where functions $f^{\pm}$ are proper rational functions. The embedding of the rational distributions subspace into the rational mnemofunctions algebra on $\mathbb{R}$ was built by the mean of mapping $R_{a}(f)=f_{\varepsilon}(x)=f^{+}(x+i\varepsilon) - f^{-}(x-i\varepsilon)$. A complete description of this algebra was given. Its generators were singled out; the multiplication rule of distributions in this algebra was formulated explicitly. Known cases when product of distributions is a distribution were analyzed by the terms of rational mnemofunctions theory. The conditions under which the product of arbitrary rational distributions is associated with a distribution were formulated.