The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

We provide a concrete class of rings in which there exists a primary ideal with respect to the maximal ideal that has only one Rees valuation.

The paper is devoted to the so-called complete Leibniz algebras. It known that a Lie algebra with ideal split. We will prove this result valid for algebras whose solvable such codimension of nilradical equal number generators nilradical.