Decompositions of associative rings
by
Vladimir Kirichenko
Kiev, Ukraine

All rings are associative with 1 =/= 0, all modules are right and unitary.

A ring is called decomposable if it is a direct product of two rings, otherwise the ring is indecomposable.

A ring A is called a finitely decomposable ring (FD-ring) if it is a finite direct product of indecomposable rings.

Let A be an associative ring, PrA be its prime radical. The quotient ring A/PrA is called the diagonal of the ring A.

If a quotient ring [`A]=A/I is a finite direct product of indecomposable rings then A is called the ring with the finite decomposable diagonal (FDD-ring). For every FDD-ring A is defined prime quiver PQ(A) (see [1]).

We consider relations between decompositions of FDD-rings and properties of its prime quivers.

References

1. Kirichenko V.V., Mashchenko L.Z. Yaremenko Yu.V. Decomposition theorems for associative rings, Problems in Algebra.v.11, Gomel Univ. Press. 1997, 42-47.

Date received: July 26, 2000