2019
Том 71
№ 11

# Gorbachuk E. L.

Articles: 5
Brief Communications (English)

### $I$-Radicals, Their Lattices, and Some Classes of Rings

Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 1016-1019

We describe some I-radicals in the categories of modules over semilocal rings. We give a characterization of rings over which the set of I-radicals coincides with the set of hereditary idempotent radicals. We prove that the lattices of I-radicals in the categories of modules over Morita-equivalent rings are isomorphic.

Brief Communications (Ukrainian)

### Existence of Cesàro limit of bounded solution of evolution equation in banach space

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1279–1280

An existence criterion for the Cesàro limit $$\left( {\mathop {\lim }\limits_{t \to \infty } \frac{1}{t}\int\limits_0^t {y(\xi )d\xi } } \right)$$ of a bounded solution $y(t)$ of the problem $dy(t)/dt = Ay(t), y(0)=y_0, t ∈ [O, ∞)$, where $A$ is a closed linear operator with dense domain of definition $D(A)$ in a reflexive Banach space $E$, is obtained under the condition that there exists a sufficiently small interval $(O, δ)$ belonging to the set of the regular points $ρ(A)$ of the operator $A$.

Article (Ukrainian)

### Axiomatizability of radical and semisimple classes of modules and Abelian groups

Ukr. Mat. Zh. - 1982. - 34, № 2. - pp. 151-157

Article (Ukrainian)