On some distributive algebras
2004jbv | Solovey L.G.

The examined type of sets, that are not rings, but in some sense are close to them. These sets are called 'Hyper-rings'. They consist of several additive groups, that intersect each over at the zero only. Yet, they are multiplicative groupoids (or groups, excluding the zero). The distributive laws are fulfilled.
Rings (and in particular the bodies and the fields) are the special case of the concerned sets. The given examples witness that such sets are highly disseminated. So, the idea that the real physical values may be "layed" in the ring is wrong, because they are subset of hyper-ring.
The real hyper-rings with unity can not be reduced to rings. Their additive groups are vector spaces, and they may be treated as a generalized Hyper-complex systems, in which we include the real binary (provided with summation and multiplication) distributive algebraic structures with neutral element, where the number of included vector spaces is more than one and finite.
The example of hyper-rings, suggesting that scrutiny of them is worth-able, are the second order matrices, that are mostly like unitary matrixes, but normalized not by unity. They are normalized by an arbitrary non-negative number. The complex numbers and the quaternions may be represented with such matrixes while they are the ones subspace.

English:		Russian: