2019
Том 71
№ 6

# Bondarenko V. M.

Articles: 5
Article (Ukrainian)

### Indecomposable and isomorphic objects in the category of monomial matrices over a local ring

Ukr. Mat. Zh. - 2017. - 69, № 7. - pp. 889-904

We study the indecomposability and isomorphism of objects from the category of monomial matrices $\mathrm{M}\mathrm{m}\mathrm{a}\mathrm{t}(K)$ over a commutative local principal ideal ring $K$ (whose objects are square monomial matrices and the morphisms from $X$ to $Y$ are the matrices $C$ such that $XC = CY$). We also study the subcategory $\mathrm{M}\mathrm{m}\mathrm{a}\mathrm{t}_0(K)$ of the category $\mathrm{M}\mathrm{m}\mathrm{a}\mathrm{t}(K)$ with the same objects and only those morphisms that are monomial matrices.

Article (Russian)

### Local deformations of positive-definite quadratic forms

Ukr. Mat. Zh. - 2012. - 64, № 7. - pp. 892-907

We give a complete description of real numbers that are $P$-limit numbers for integer-valued positive-definite quadratic forms with unit coefficients of the squares. It is shown that each of these $P$-limit numbers is realized in the Tits quadratic form of a Dynkin diagram.

Article (Russian)

### Description of posets critical with respect to the nonnegativity of the quadratic Tits form

Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 611-624

We present the complete description of finite posets whose Tits form is not nonnegative but all proper subsets of which have nonnegative Tits forms. A similar result for positive forms was obtained by the authors earlier.

Article (Russian)

### $(\min, \max)$-equivalence of posets and nonnegative Tits forms

Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1157–1167

We study the relationship between the (min, max)-equivalence of posets and properties of their quadratic Tits form related to nonnegative definiteness. In particular, we prove that the Tits form of a poset S is nonnegative definite if and only if the Tits form of any poset $(\min, \max)$-equivalent to S is weakly nonnegative.

Obituaries (Ukrainian)

### Andrei Reuter (1937-2006)

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