1.6.28 Fields, Groups, Rings

Problem: For the given ring \( K \) and its subring \( H \) : a) describe (left) cosets; b) find out whether the quotient ring is defined; c) if a quotient ring is defined, give an example of an isomorphic ring; \( K=\left(\mathbb{R}^{\infty},+, \cdot\right) \) is a ring of all sequences of real numbers, \( \quad H=\left\{\left\{x_{n}\right\} \in \mathbb{R}^{\infty}: x_{1}=\cdots=x_{n}=0\right\} \) ( \( n \) is fixed).