Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-01-31
On the 2-absorbing submodules and zero-divisor graph of equivalence classes of zero divisors
Shiroyeh Payrovi, Yasaman SadatrasulAbstract : Let $R$ be a commutative ring, $M$ be a Noetherian $R$-module, and $N$ a 2-absorbing submodule of $M$ such that $r(N :_{R} M)= \mathfrak p$ is a prime ideal of $R$. The main result of the paper states that if $N=Q_1\cap\cdots\cap Q_n$ with $r(Q_i:_RM)=\mathfrak p_i$, for $i=1,\ldots, n$, is a minimal primary decomposition of $N$, then the following statements are true. \begin{itemize} \item[(i)] $\mathfrak p=\mathfrak p_k$ for some $1 \leq k \leq n$. \item[(ii)] For each $j=1,\ldots,n$ there exists $m_j \in M$ such that ${\mathfrak p}_j=(N :_{R} m_{j})$. \item[(iii)] For each $i,j=1,\ldots,n$ either $\mathfrak p_{i} \subseteq \mathfrak p_{j}$ or $\mathfrak p_{j} \subseteq \mathfrak p_{i}$. \end{itemize} Let $\Gamma_E(M)$ denote the zero-divisor graph of equivalence classes of zero divisors of $M$. It is shown that $\{Q_1\cap\cdots\cap Q_{n-1}, Q_1\cap\cdots\cap Q_{n-2},\ldots , Q_1\}$ is an independent subset of $V(\Gamma_E(M))$, whenever the zero submodule of $M$ is a 2-absorbing submodule and $Q_1\cap\cdots\cap Q_n=0$ is its minimal primary decomposition. Furthermore, it is proved that $\Gamma_E(M)[(0 :_{R} M)]$, the induced subgraph of $\Gamma_E(M)$ by $(0 :_{R} M)$, is complete.
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2022-10-31
The independence and independent dominating numbers of the total graph of a finite commutative ring
Baha' Abughazaleh, Omar AbedRabbu AbughneimAbstract : Let $R$ be a finite commutative ring with nonzero unity and let $Z(R)$ be the zero divisors of $R$. The total graph of $R$ is the graph whose vertices are the elements of $R$ and two distinct vertices $x,y\in R$ are adjacent if $x+y\in Z(R)$. The total graph of a ring $R$ is denoted by $\tau (R)$. The independence number of the graph $\tau (R)$ was found in \cite{Nazzal}. In this paper, we again find the independence number of $\tau (R)$ but in a different way. Also, we find the independent dominating number of $\tau (R)$ . Finally, we examine when the graph $\tau (R)$ is well-covered.
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2022-10-31
Classification of Solvable Lie groups whose non-trivial coadjoint orbits are of Codimension $1$
Hieu Van Ha, Duong Quang Hoa, Vu Anh LeAbstract : We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.
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2022-07-31
Commutativity criteria of prime rings involving two endomorphisms
Souad Dakir, Abdellah Mamouni, Mohammed TamekkanteAbstract : This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.
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2022-10-31
On the semi-local convergence of contraharmonic-mean Newton's method (CHMN)
Ioannis K. Argyros, Manoj Kumar SinghAbstract : The main objective of this work is to investigate the study of the local and semi-local convergence of the contraharmonic-mean Newton's method (CHMN) for solving nonlinear equations in a Banach space. We have performed the semi-local convergence analysis by using generalized conditions. We examine the theoretical results by comparing the CHN method with the Newton's method and other third order methods by Weerakoon et al.~using some test functions. The theoretical and numerical results are also supported by the basins of attraction for a selected test function.
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2023-04-30
H-quasi-hemi-slant submersions
Sumeet Kumar, Sushil Kumar, Rajendra Prasad, Aysel Turgut VanliAbstract : In this paper, h-quasi-hemi-slant submersions and almost h-quasi-hemi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds are introduced. Fundamental results on h-quasi-hemi-slant submersions: the integrability of distributions, geometry of foliations and the conditions for such submersions to be totally geodesic are investigated. Moreover, some non-trivial examples of the h-quasi-hemi-slant submersion are constructed.
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2023-01-31
The $u$-$S$-weak global dimensions of commutative rings
Xiaolei ZhangAbstract : In this paper, we introduce and study the $u$-$S$-weak global dimension $u$-$S$-w.gl.dim$(R)$ of a commutative ring $R$ for some multiplicative subset $S$ of $R$. Moreover, the $u$-$S$-weak global dimensions of factor rings and polynomial rings are investigated.
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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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2022-10-31
Circle approximation using parametric polynomial curves of high degree in explicit form
Young Joon AhnAbstract : In this paper we present a full circle approximation method using parametric polynomial curves with algebraic coefficients which are curvature continuous at both endpoints. Our method yields the $n$-th degree parametric polynomial curves which have a total number of $2n$ contacts with the full circle at both endpoints and the midpoint. The parametric polynomial approximants have algebraic coefficients involving rational numbers and radicals for degree higher than four. We obtain the exact Hausdorff distances between the circle and the approximation curves.
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2022-10-31
Sharp estimates on the third order Hermitian-Toeplitz determinant for Sakaguchi classes
Sushil Kumar, Virendra KumarAbstract : In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.
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Geometric inequalities for warped products submanifolds in generalized complex space forms
Mohd Aquib, Mohd Aslam, Michel Nguiffo Boyom, Mohammad Hasan Shahid
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Notes on $(LCS)_n$-manifolds satisfying certain conditions
Shyam Kishor, Pushpendra Verma
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Semi-neutral groupoids and $BCK$-algebras
Hee Sik Kim, Joseph Neggers, Young Joo Seo
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The dimension graph for modules over commutative rings
Shiroyeh Payrovi
Commun. Korean Math. Soc. 2023; 38(3): 733-740
https://doi.org/10.4134/CKMS.c220273
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Nonnil-$S$-coherent rings
Najib Mahdou, El Houssaine Oubouhou
Commun. Korean Math. Soc. 2024; 39(1): 45-58
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Geometry of generalized Berger-type deformed metric on $B$-manifold
ABDERRAHIM ZAGANE
Commun. Korean Math. Soc. 2023; 38(4): 1281-1298
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Jordan $\mathcal{G}_n$-derivations on path algebras
Abderrahim Adrabi, Driss Bennis, Brahim Fahid
Commun. Korean Math. Soc. 2022; 37(4): 957-967
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Spacetimes admitting divergence free $m$-projective curvature tensor
Uday Chand De, Dipankar Hazra
Commun. Korean Math. Soc. 2024; 39(1): 201-210
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