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Mehmet Özen

Publications and source records attributed to Mehmet Özen.

4 recordsLinked to original sources
arXiv2025

New Results On $S-r-$ideals in Commutative Rings

This article studies the notion of $S-r-$ideals in commutative ring $H$, where $S$ is a multiplicatively closed subset of $H$. Some basic properties of $S-r-$ideals are given. Various characterizations of $S-r-$ideals are presented. Also, $S-uz-$ring is defined and it is proved that $H$ is an $S-uz-$ring if and only if every maximal ideal disjoint from $S$ is an $S-r-$ideal provided $S$ is finite. In addition, the $S-r-$ideal concept is examined in amalgamation and trivial extension. Finally, $S-r-$ideals are studied in polynomial rings and it is investigated that when $A[x]$ is an $S-r-$ideal of $H[x].$

math.AC↗
arXiv2024

On Regular Fusible Modules

In this article, we introduce the notion of regular fusible modules. Let $R$ be a ring with an identity and $M$ an $R$-module. An element $0\neq m\in M$ is said to be regular fusible if there exists $r\in R$, a non zero-divisor of $M$, such that $mr$ can be written as the sum of a torsion element and a torsion free element in $M$. $M$ is called regular fusible if every nonzero element of $M$ is regular fusible. We characterize regular fusible modules in terms of fusible modules. In addition, we show that a regular fusible module over a right duo ring is reduced and nonsingular. Moreover, we study the regular fusible property under Cartesian product, trivial extension ring, and module of a fractions. Also, we characterize division rings in terms of fusible modules.

math.RA↗
arXiv2019

Self-Dual Skew Cyclic Codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$

In this paper, we give conditions for the existence of Hermitian self-dual $Θ-$cyclic and $Θ-$negacyclic codes over the finite chain ring $\mathbb{F}_q+u\mathbb{F}_q$. By defining a Gray map from $R=\mathbb{F}_q+u\mathbb{F}_q$ to $\mathbb{F}_{q}^{2}$, we prove that the Gray images of skew cyclic codes of odd length $n$ over $R$ with even characteristic are equivalent to skew quasi-twisted codes of length $2n$ over $\mathbb{F}_q$ of index $2$. We also extend an algorithm of Boucher and Ulmer \cite{BF3} to construct self-dual skew cyclic codes based on the least common left multiples of non-commutative polynomials over $\mathbb{F}_q+u\mathbb{F}_q$.

cs.IT↗