SEMI-ISOMETRIC ISOMORPHISM AND COMPLETION OF PSEUDONORMED RINGS
The article is devoted to the study of the problem of the keeping of a semi-isometric isomorphism (semi-isometric on the left, semi-isometric on the right) when taking the completion of pseudonormed rings. It’s shown that a semi-isometric isomorphism (semi-isometric on the left, semi-isometric on the right) is saved when taking the completion of pseudonormed rings, if the pseudonormed ring (R, ξ) has an element that is not a topological zero divisor (right topological zero divisor, left topological zero divisor).