Abstract In this paper we adopt an alternative, analytical approach to Arnol’d problem [4] about the existence of closed and embedded K -magnetic geodesics in round 2-sphere $${\mathbb {S}}^2$$ S 2 , where $$K: {\mathbb {S}}^2 \rightarrow {R}}$$ <...

Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.