Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2024-01-31
Generalized derivations in ring with involution involving symmetric and skew symmetric elements
Souad DAKIR, Hajar EL MIR, Abdellah MAMOUNIAbstract : In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
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2024-01-31
3-Hom-Lie superbialgebras and 3-Hom-Lie classical Yang-Baxter equations
Issam Bartouli, Imed Basdouri, Gaith Chaabane, Mohamed Fadous, Jean LerbetAbstract : 3-Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3-ary version of the Yang-Baxter equation, called the super 3-Lie classical Hom-Yang-Baxter equation (3-Lie CHYBE), which is a general form of 3-Lie classical Yang-Baxter equation and prove that the superbialgebras induced by the solutions of the super 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie superbialgebras.
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2024-01-31
Cyclic codes of length $p^s$ over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$
Roghayeh Mohammadi Hesari, Masoumeh Mohebbei, Rashid Rezaei, Karim SameiAbstract : Let $R_e=\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$, where $p$ is a prime number, $ e $ is a positive integer and $u^e=0$. In this paper, we first characterize the structure of cyclic codes of length $p^s$ over $R_e$. These codes will be classified into $2^e $ distinct types. Among other results, in the case that $e=4$, the torsion codes of cyclic codes of length $ p^s $ over $ R_4$ are obtained. Also, we present some examples of cyclic codes of length $p^s $ over $R_e$.
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2024-01-31
Nonnil-$S$-coherent rings
Najib Mahdou, El Houssaine OubouhouAbstract : Let $R$ be a commutative ring with identity. If the nilpotent radical $Nil(R)$ of $R$ is a divided prime ideal, then $R$ is called a $\phi$-ring. Let $R$ be a $\phi$-ring and $S$ be a multiplicative subset of $R$. In this paper, we introduce and study the class of nonnil-$S$-coherent rings, i.e., the rings in which all finitely generated nonnil ideals are $S$-finitely presented. Also, we define the concept of $\phi$-$S$-coherent rings. Among other results, we investigate the $S$-version of Chase's result and Chase Theorem characterization of nonnil-coherent rings. We next study the possible transfer of the nonnil-$S$-coherent ring property in the amalgamated algebra along an ideal and the trivial ring extension.
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2024-01-31
The homological properties of regular injective modules
Wei Qi, Xiaolei ZhangAbstract : Let $R$ be a commutative ring. An $R$-module $E$ is said to be regular injective provided that $\Ext_R^1(R/I,E)=0$ for any regular ideal $I$ of $R$. We first show that the class of regular injective modules have the hereditary property, and then introduce and study the regular injective dimension of modules and regular global dimension of rings. Finally, we give some homological characterizations of total rings of quotients and Dedekind rings.
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2024-01-31
Some remarks on $S$-valuation domains
Ali Benhissi, Abdelamir DabbabiAbstract : Let $A$ be a commutative integral domain with identity element and $S$ a multiplicatively closed subset of $A$. In this paper, we introduce the concept of $S$-valuation domains as follows. The ring $A$ is said to be an $S$-valuation domain if for every two ideals $I$ and $J$ of $A$, there exists $s\in S$ such that either $sI\subseteq J$ or $sJ\subseteq I$. We investigate some basic properties of $S$-valuation domains. Many examples and counterexamples are provided.
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2024-01-31
Results of 3-derivations and commutativity for prime rings with involution involving symmetric and skew symmetric components
Hanane AHARSSI, Kamal CHARRABI, Abdellah MAMOUNIAbstract : This article examines the connection between 3-derivations and the commutativity of a prime ring $R$ with an involution $\ast$ that fulfills particular algebraic identities for symmetric and skew symmetric elements. In practice, certain well-known problems, such as the Herstein problem, have been studied in the setting of three derivations in involuted rings.
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2024-01-31
On strongly quasi $J$-ideals of commutative rings
El Mehdi Bouba
, Yassine EL-khabchi, Mohammed Tamekkante Abstract : Let $R$ be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi $J$-ideals lying properly between the class of $J$-ideals and the class of quasi $J$-ideals. A proper ideal $I$ of $R$ is called a strongly quasi $J$-ideal if, whenever $a$, $b\in R$ and $ab\in I$, then $a^{2}\in I$ or $b\in {\rm Jac}(R)$. Firstly, we investigate some basic properties of strongly quasi $J$-ideals. Hence, we give the necessary and sufficient conditions for a ring $R$ to contain a strongly quasi $J$-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi $J$-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.
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2024-01-31
On a uniqueness question of meromorphic functions and partial shared values
Imrul Kaish, Rana MondalAbstract : In this paper, we prove a uniqueness theorem of non-constant meromorphic functions of hyper-order less than $1$ sharing two values CM and two partial shared values IM with their shifts. Our result in this paper improves and extends the corresponding results from Chen-Lin \cite{CL2016}, Charak-Korhonen-Kumar \cite{CKK2016}, Heittokangas-Korhonen-Laine-Rieppo-Zhang \cite{HKLRZ2009} and Li-Yi \cite{LY2016}. Some examples are provided to show that some assumptions of the main result of the paper are necessary.
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2024-01-31
Some results related to differential-difference counterpart of the Br\"{u}ck conjecture
Md. Adud, BIKASH CHAKRABORTYAbstract : In this paper, our focus is on exploring value sharing \linebreak problems related to a transcendental entire function $f$ and its associated differential-difference polynomials. We aim to establish some results which are related to differential-difference counterpart of the Br\"{u}ck conjecture.
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2024-01-31
An example for the non-stability of multi-additive-quadratic-cubic mappings
Abasalt BodaghiAbstract : In this paper, we improve Corollary 1 of \cite{bras} and then present an example to show that the assertion in the mentioned corollary can not be valid in the singularity case.
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2024-01-31
The class of $p$-demicompact operators on lattice normed spaces
Imen Ferjani, Bilel KrichenAbstract : In the present paper, we introduce a new class of operators called $p$-demicompact operators between two lattice normed spaces $X$ and $Y$. We study the basic properties of this class. Precisely, we give some conditions under which a $p$-bounded operator be $p$-demicompact. Also, a sufficient condition is given, under which each $p$-demicompact operator has a modulus which is $p$-demicompact. Further, we put in place some properties of this class of operators on lattice normed spaces.
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2024-01-31
On the generalized Ornstein-Uhlenbeck operators with regular and singular potentials in weighted $L^{p}$-spaces
Imen MetouiAbstract : In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials \begin{align*} A_{\Phi,G,V,c} = \Delta-\nabla \Phi\cdot\nabla+G\cdot \nabla-V+c|x|^{-2} \end{align*} with a suitable domain generates a quasi-contractive, positive and analytic $C_{0}$-semigroup in $L^{p}(\mathbb{R}^{N},e^{-\Phi(x)}dx)$, $1
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2024-01-31
Conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with Schouten-van Kampen connection
PARDIP MANDAL, MOHAMMAD HASAN SHAHID, SARVESH KUMAR YADAVAbstract : The main object of the present paper is to study conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection. Further, we obtain the result when paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection satisfying the condition $\overset{\star}{C}(\xi,U)\cdot\overset{\star}{S}=0$. Finally we characterized concircular curvature tensor on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection.
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2024-01-31
Generalized $\eta$-Ricci solitons on para-Kenmotsu manifolds associated to the Zamkovoy connection
Shahroud azamiAbstract : In this paper, we study para-Kenmotsu manifolds admitting generalized $\eta$-Ricci solitons associated to the Zamkovoy connection. We provide an example of generalized $\eta$-Ricci soliton on a para-Kenmotsu manifold to prove our results.
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2024-01-31
Intrinsic theory of $C^v$-reducibility in Finsler Geometry
Salah Gomaa Elgendi, Amr SoleimanAbstract : In the present paper, following the pullback approach to Finsler geometry, we study intrinsically the $C^v$-reducible and generalized $C^v$-reducible Finsler spaces. Precisely, we introduce a coordinate-free formulation of these manifolds. Then, we prove that a Finsler manifold is $C^v$-reducible if and only if it is $C$-reducible and satisfies the $\mathbb{T}$-condition. We study the generalized $C^v$-reducible Finsler manifold with a scalar $\pi$-form $\mathbb{A}$. We show that a Finsler manifold $(M,L)$ is generalized $C^v$-reducible with $\mathbb{A}$ if and only if it is $C$-reducible and $\mathbb{T}=\mathbb{A}$. Moreover, we prove that a Landsberg generalized $C^v$-reducible Finsler manifold with a scalar $\pi$-form $\mathbb{A}$ is Berwaldian. Finally, we consider a special $C^v$-reducible Finsler manifold and conclude that a Finsler manifold is a special $C^v$-reducible if and only if it is special semi-$C$-reducible with vanishing $\mathbb{T}$-tensor.
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2024-01-31
Spacetimes admitting divergence free $m$-projective curvature tensor
Uday Chand De, Dipankar HazraAbstract : This paper is concerned with the study of spacetimes satisfying $\mathrm{div}\mathcal{M}=0$, where ``div" denotes the divergence and $\mathcal{M}$ is the $m$-projective curvature tensor. We establish that a perfect fluid spacetime with $\mathrm{div}\mathcal{M}=0$ is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with $\mathrm{div}\mathcal{M}=0$ represents a generalized Robertson-Walker spacetime.
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2024-01-31
Some characterizations of conics and hypersurfaces with centrally symmetric hyperplane sections
Shin-Ok Bang, Dong Seo Kim, Dong-Soo Kim, Wonyong KimAbstract : Parallel conics have interesting area and chord properties. In this paper, we study such properties of conics and conic hypersurfaces. First of all, we characterize conics in the plane with respect to the above mentioned properties. Finally, we establish some characterizations of hypersurfaces with centrally symmetric hyperplane sections.
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2024-01-31
RNA foldings and stuck knots
Jose Ceniceros, Mohamed Elhamdadi, Josef Komissar, Hitakshi LahraniAbstract : We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots emphasize a biomolecule's entanglement while ignoring their intrachain interactions. We remedy this by using stuck knots and links, which provide a way to emphasize both their entanglement and intrachain interactions. We first give a generating set of the oriented stuck Reidemeister moves for oriented stuck links. We then introduce an algebraic structure to axiomatize the oriented stuck Reidemeister moves. Using this algebraic structure, we define a coloring counting invariant of stuck links and provide explicit computations of the invariant. Lastly, we compute the counting invariant for arc diagrams of RNA foldings through the use of stuck link diagrams.
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2024-01-31
Skew brace enhancements and virtual links
Melody Chang, Sam NelsonAbstract : We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new invariants: a single-variable polynomial using skew brace ideals and a two-variable polynomial using the skew brace group structures. We provide examples to show that the new invariants are not determined by the counting invariant and hence are proper enhancements.
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2024-01-31
Terminal spaces of monoids
Amartya GoswamiAbstract : The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to $r$-strongly irreducible $r$-ideals (endowed with Zariski topologies) of monoids, called terminal spaces. We show that terminal spaces are $T_0$, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. We characterize $r$-arithmetic monoids in terms of terminal spaces. Finally, we provide necessary and sufficient conditions for the subspaces of $r$-maximal $r$-ideals and $r$-prime $r$-ideals to be dense in the corresponding terminal spaces.
January, 2024 | Volume 39, No. 1
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The homology regarding to e-exact sequences
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