2019
Том 71
№ 9

# Nazarova L. A.

Articles: 9
Article (Russian)

### The Norm of a Relation, Separating Functions, and Representations of Marked Quivers

Ukr. Mat. Zh. - 2002. - 54, № 6. - pp. 808-840

We consider numerical functions that characterize Dynkin schemes, Coxeter graphs, and tame marked quivers.

Brief Communications (Russian)

### Finitely Represented $K$-Marked Quivers

Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 550-555

We present necessary and sufficient conditions for the finite representability of K-marked quivers.

Article (Russian)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1363-1396

A criterion of finite representability of dyadic sets is presented.

Article (English)

### Finitely represented dyadic sets and their multielementary representations

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1465–1477

We obtain the direct reduction of representations of a dyadic set S such that |Ind C(S)| < ∞ to the bipartite case.

Article (Russian)

### Elementary and multielementary representations of vectroids

Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1451–1477

We prove that every finitely represented vectroid is determined, up to an isomorphism, by its completed biordered set. Elementary and multielementary representations of such vectroids (which play a central role for biinvolutive posets) are described.

Article (English)

### Tame and wild subspace problems

Ukr. Mat. Zh. - 1993. - 45, № 3. - pp. 313–352

Assume that $B$ is a finite-dimensional algebra over an algebraically closed field $k$, $B_d = \text{Spec} k[B_d]$ is the affine algebraic scheme whose $R$-points are the $B ⊗_k k[B_d]$-module structures on $R^d$, and $M_d$ is a canonical $B ⊗_k k[B_d]$-module supported by $k[Bd^]d$. Further, say that an affine subscheme $Ν$ of $B_d$ isclass true if the functor $F_{gn} ∶ X → M_d ⊗_{k[B]} X$ induces an injection between the sets of isomorphism classes of indecomposable finite-dimensional modules over $k[Ν]$ and $B$. If $B_d$ contains a class-true plane for some $d$, then the schemes $B_e$ contain class-true subschemes of arbitrary dimensions. Otherwise, each $B_d$ contains a finite number of classtrue puncture straight lines $L(d, i)$ such that for eachn, almost each indecomposable $B$-module of dimensionn is isomorphic to some $F_{L(d, i)} (X)$; furthermore, $F_{L(d, i)} (X)$ is not isomorphic to $F_{L(l, j)} (Y)$ if $(d, i) ≠ (l, j)$ and $X ≠ 0$. The proof uses a reduction to subspace problems, for which an inductive algorithm permits us to prove corresponding statements.

Article (Ukrainian)

### Integral p-adic representations and representations over a ring of residue classes

Ukr. Mat. Zh. - 1967. - 19, № 2. - pp. 125–126

Brief Communications (Russian)

### Integral representations of asign - variable group of the fourth degree

Ukr. Mat. Zh. - 1963. - 15, № 4. - pp. 437-444

Article (Russian)

### Whole-number representations of a symmetrical group of third degree

Ukr. Mat. Zh. - 1962. - 14, № 3. - pp. 271-288

The authors discuss whole-number representations to a symmetrica! group of the third degree. It is shown that there exists only a finite number, i. e. ten, prime representations of this group. The dimensions of the prime representations do not exceed the order of the group.
It is further shown that the factoring of any representation into a direct sum of primes is univalent.
Thus the first example has been given of a complete description of whole-number representations of a non-commutative group.