On Diagonal Nonconstant Right-Symmetric Algebras of Matrix Type M(F)

We describe the right-symmetric algebrasof matrix type M(F) over a field F of characteristic 0 such thatthe left action of the orthogonal idempotents of M(F) is diagonalizable,and the right-module part W includes no constant bichains. We construct some wide class of nonassociative algebras (Formula presented.), where W is a subalgebra anda right module over an associative algebra A. We give a criterion for these algebras to be right-symmetric. Assuming that WA=W, we show that the algebrasof this class are either simple or local. We exhibit some examples of simple right-symmetric algebras andright-symmetric algebras withoutnilpotent right ideals whose right-module partis not an irreducible module over M(F).