2019
Том 71
№ 7

# Kirichenko V. V.

Articles: 14
Article (Ukrainian)

### Topological conjugate piecewise linear unimodal mappings of an interval into itself

Ukr. Mat. Zh. - 2016. - 68, № 2. - pp. 217-226

Let $f, g : [0, 1] \rightarrow [0, 1]$ be a pair of continuous piecewise linear unimodal mappings and let $f$ be defined as follows: $f(x) = 2x$ for $x \leq 1/2$ and $f(x) = 2 - 2x$ for $x > 1/2$. Also let $h : [0, 1] \rightarrow [0, 1]$ be a piecewise differentiable homeomorphism such that $fh = hg$. Then $h$ is piecewise linear and the mapping $f$ completely determines $g$ and $h$, together with the ascending or descending monotone parts of $g$.

Anniversaries (Ukrainian)

### Dmytro Ivanovych Martynyuk (on the 70th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 571-573

Article (Ukrainian)

### Simple strongly connected quivers and their eigenvectors

Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 291-306

We study the relationship between the isomorphism of quivers and properties of their spectra. It is proved that two simple strongly connected quivers with at most four vertices are isomorphic to one another if and only if their characteristic polynomials coincide and their left and right normalized positive eigenvectors that correspond to the index can be obtained from one another by the permutation of their coordinates. An example showing that this statement is not true for quivers with five vertices is given.

Article (English)

### Rings with finite decomposition of identity

Ukr. Mat. Zh. - 2011. - 63, № 3. - pp. 319-340

A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semidistributive semiperfect ring is distributive. An application of decompositions of identity to groups of units is given.

Article (Ukrainian)

### Semiperfect ipri-rings and right Bézout rings

Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 612–624

We present a survey of some results on ipri-rings and right Bézout rings. All these rings are generalizations of principal ideal rings. From the general point of view, decomposition theorems are proved for semiperfect ipri-rings and right Bézout rings.

Obituaries (Ukrainian)

### Andrei Reuter (1937-2006)

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1584-1585

Article (English)

### Quasi-Frobenius Rings and Nakayama Permutations of Semiperfect Rings

Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 919-930

We say that ${\mathcal{A}}$ is a ring with duality for simple modules, or simply a DSM-ring, if, for every simple right (left) ${\mathcal{A}}$ -module U, the dual module U* is a simple left (right) ${\mathcal{A}}$ -module. We prove that a semiperfect ring is a DSM-ring if and only if it admits a Nakayama permutation. We introduce the notion of a monomial ideal of a semiperfect ring and study the structure of hereditary semiperfect rings with monomial ideals. We consider perfect rings with monomial socles.

Chronicles (Ukrainian)

### Second international Algebraic Conference in Ukraine dedicated to the memory of Professor L. A. Kaluzhnin

Ukr. Mat. Zh. - 2000. - 52, № 4. - pp. 574-576

Article (Russian)

### Multiserial rings

Ukr. Mat. Zh. - 1996. - 48, № 9. - pp. 1223–1235

We introduce the notion of multiserial (n-serial) rings and study their properties. The second-order minors of such rings are investigated. We also find all possible forms of quivers for Noetherian and hereditaryn-serial rings and describe the structure of semiprime and hereditaryn-serial rings.

Article (Ukrainian)

### Noetherian biserial rings

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 435-440

Article (Ukrainian)

### Semiinherent semichain rings

Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 156-161

Article (Ukrainian)

### Diserial rings

Ukr. Mat. Zh. - 1986. - 38, № 6. - pp. 718–723

Article (Ukrainian)

### Hereditary orders

Ukr. Mat. Zh. - 1968. - 20, № 2. - pp. 246–248

Article (Ukrainian)

### Epresentation of rings lying in a matrix algebra of second order

Ukr. Mat. Zh. - 1967. - 19, № 3. - pp. 107–112