arXiv subjects

Doniyor Yazdonov

Publications and source records attributed to Doniyor Yazdonov.

3 recordsLinked to original sources

arXiv2026

On algebraic and arithmetic properties of monoids of product-$K$ sequences

Let $G$ be a group and $K$ be a normal subgroup of $G$. A sequence over $G$ is a finite collection of terms from $G$, where repetition is allowed, and the order is disregarded. A product-$K$ sequence is a sequence whose terms can be ordered such that their product in $G$ belongs to $K$. The set $\mathcal B_K (G)$ of all product-$K$ sequences over $G$ forms a monoid, called the monoid of product-$K$ sequences, under the operation of sequence concatenation. In this paper, we investigate the algebraic and arithmetic properties of the monoid $\mathcal B_K (G)$. Among our main results, we provide precise characterizations of when the monoid $\mathcal B_K (G)$ satisfies key properties, namely being a (transfer) Krull, seminormal, or (half-)factorial. Our results generalize existing frameworks, making them applicable to both the classical abelian and the more recently developed non-abelian settings.

math.GR↗

arXiv2026

Topological insights into Monoids and Module systems

In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.

math.AC↗

arXiv2026

On the structure of length sets with maximal elasticity

Let $H$ be a Krull monoid with finite class group $G$ and suppose that each class contains a prime divisor. Then every non-unit $a \in H$ has a factorization into atoms, say $a=u_1 \cdot\ldots \cdot u_k$ where $k$ is the factorization length and $u_1, \ldots, u_k$ are atoms of $H$. The set $\mathsf L (a)$ of all possible factorizaton lengths is the length set of $a$, and $ρ(H) = \sup \{ \max \mathsf L (a)/\min \mathsf L (a) \colon a \in H \}$ is the elasticity of $H$. We study the structure of length sets of elements with maximal elasticity and show that, in general, these length sets are intervals.

math.AC↗