Ideal ring extensions and trusses

It is shown that there a close relationship between ideal extensions of rings and trusses, is, sets with semigroup operation distributing over ternary abelian heap operation. Specifically, truss can be associated to every element an extension ring projects down idempotent in the extending ring; weak equivalence yields isomorphism corresponding trusses. Furthermore, classes by integers are one-to-one correspondence trusses up given translation. Conversely, any T this one associate its which embedded as truss. Consequently understood arising from integers. The key role played interpretation defined double homothetisms Redei (L. (1952) [24]) or self-permutable bimultiplications Mac Lane (S. (1958) [18]), integral homothetic extensions. used classify fully zero multiplication trivial annihilators.