Given a local ring $(R,\mathfrak{m})$ and an elliptic curve $E(R/\mathfrak{m})$, we define loops as the points of $\mathbb{P}^2(R)$ projecting to $E$ under canonical modulo-$\mathfrak{m}$ reduction, endowed with operation that extends curve's addition. While their subset satisfying Weierstrass equation is group, these larger objects are proved be power associative abelian algebraic loops, which...