Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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  • 2023-01-31

    Conformal hemi-slant submersions from cosymplectic manifolds

    Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma

    Abstract : The main goal of the paper is the introduction of the notion of conformal hemi-slant submersions from almost contact metric manifolds onto Riemannian manifolds. It is a generalization of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. Our main focus is conformal hemi-slant submersion from cosymplectic manifolds. We tend also study the integrability of the distributions involved in the definition of the submersions and the geometry of their leaves. Moreover, we get necessary and sufficient conditions for these submersions to be totally geodesic, and provide some representative examples of conformal hemi-slant submersions.

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  • 2023-01-31

    The homology regarding to e-exact sequences

    Ismael Akray, Amin Mahamad Zebari

    Abstract : Let $R$ be a commutative ring with identity. Let $R$ be an integral domain and $M$ a torsion-free $R$-module. We investigate the relation between the notion of e-exactness, recently introduced by Akray and Zebari \cite{a a}, and generalized the concept of homology, and establish a relation between e-exact sequences and homology of modules. We modify some applications of e-exact sequences in homology and reprove some results of homology with e-exact sequences such as horseshoe lemma, long exact sequences, connecting homomorphisms and etc. Next, we generalize two special drived functor $Tor$ and $Ext$, and study some properties of them.

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  • 2023-01-31

    On Noetherian pseudo-prime spectrum of a topological le-module

    Anjan Kumar Bhuniya, Manas Kumbhakar

    Abstract : An le-module $M$ over a commutative ring $R$ is a complete lattice ordered additive monoid $(M, \leqslant, +)$ having the greatest element $e$ together with a module like action of $R$. This article characterizes the le-modules $_RM$ such that the pseudo-prime spectrum $X_M$ endowed with the Zariski topology is a Noetherian topological space. If the ring $R$ is Noetherian and the pseudo-prime radical of every submodule elements of $_{R}M$ coincides with its Zariski radical, then $X_{M}$ is a Noetherian topological space. Also we prove that if $R$ is Noetherian and for every submodule element $n$ of $M$ there is an ideal $I$ of $R$ such that $V(n) = V(Ie)$, then the topological space $X_{M}$ is spectral.

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  • 2023-07-31

    The dimension graph for modules over commutative rings

    Shiroyeh Payrovi

    Abstract : Let $R$ be a commutative ring and $M$ be an $R$-module. The dimension graph of $M$, denoted by $DG(M)$, is a simple undirected graph whose vertex set is $Z(M)\setminus {\rm Ann}(M)$ and two distinct vertices $x$ and $y$ are adjacent if and only if $\dim M/(x, y)M=\min\{\dim M/xM, \dim M/yM\}$. It is shown that $DG(M)$ is a disconnected graph if and only if (i) ${\rm Ass}(M)=\{\mathfrak p, \mathfrak q\}$, $Z(M)=\mathfrak p\cup \mathfrak q$ and ${\rm Ann}(M)=\mathfrak p\cap \mathfrak q$. (ii) $\dim M=\dim R/\mathfrak p=\dim R/\mathfrak q$. (iii) $\dim M/xM=\dim M$ for all $x\in Z(M)\setminus {\rm Ann}(M)$. Furthermore, it is shown that ${\rm diam}(DG(M))\leq 2$ and ${\rm gr}({DG(M)})=3$, whenever $M$ is Noetherian with $|Z(M)\setminus {\rm Ann}(M)| \geq 3$ and $DG(M)$ is a connected graph.

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  • 2023-04-30

    Unitary analogues of a generalized number-theoretic sum

    Traiwat Intarawong, Boonrod Yuttanan

    Abstract : In this paper, we investigate the sums of the elements in the finite set $\{x^{k}:1\leq x\leq\frac{n}{m},\gcd_u(x,n)=1\}$, where $k$, $m$ and $n$ are positive integers and $\gcd_u(x,n)$ is the unitary greatest common divisor of $x$ and $n$. Moreover, for some cases of $k$ and $m$, we can give the explicit formulae for the sums involving some well-known arithmetic functions.

  • 2023-01-31

    A question about maximal non $\phi$-chained subrings

    Atul Gaur, Rahul Kumar

    Abstract : Let $\mathcal{H}_0$ be the set of rings $R$ such that $Nil(R) = Z(R)$ is a divided prime ideal of $R$. The concept of maximal non $\phi$-chained subrings is a generalization of maximal non valuation subrings from domains to rings in $\mathcal{H}_0$. This generalization was introduced in \cite{rahul} where the authors proved that if $R \in \mathcal{H}_0$ is an integrally closed ring with finite Krull dimension, then $R$ is a maximal non $\phi$-chained subring of $T(R)$ if and only if $R$ is not local and $|[R, T(R)]|$ = $\dim (R) + 3$. This motivates us to investigate the other natural numbers $n$ for which $R$ is a maximal non $\phi$-chained subring of some overring $S$. The existence of such an overring $S$ of $R$ is shown for $3\leq n \leq 6$, and no such overring exists for $n = 7$.

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  • 2023-07-31

    Hyers-Ulam stability of fractional stochastic differential equations with random impulse

    Dumitru Baleanu, Banupriya Kandasamy, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran

    Abstract : The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.

  • 2023-07-31

    A study of differential identities on $\sigma$-prime rings

    Adnan Abbasi, Md Arshad Madni, Muzibur Rahman Mozumder

    Abstract : Let $\mathcal{R}$ be a $\sigma$-prime ring with involution $\sigma$. The main \linebreak objective of this paper is to describe the structure of the $\sigma$-prime ring $\mathcal{R}$ with involution $\sigma$ satisfying certain differential identities involving three derivations $\psi_1, \psi_2$ and $\psi_3$ such that $\psi_1[t_1,\sigma(t_1)]+[\psi_2(t_1),\psi_2(\sigma(t_1))] + [\psi_3(t_1),\sigma(t_1)]\in \mathcal{J}_Z$ for all $t_1\in \mathcal{R}$. Further, some other related results have also been discussed.

  • 2023-07-31

    $\star$-conformal Ricci solitons on almost coK\"{a}hler manifolds

    Tarak Mandal, Avijit Sarkar

    Abstract : The main intention of the current paper is to characterize certain properties of $\star$-conformal Ricci solitons on non-coK\"ahler $(\kappa,\mu)$-almost coK\"{a}hler manifolds. At first, we find that there does not exist $\star$-conformal Ricci soliton if the potential vector field is the Reeb vector field $\theta$. We also prove that the non-coK\"ahler $(\kappa,\mu)$-almost coK\"ahler manifolds admit $\star$-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist $\star$-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.

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  • 2023-07-31

    Fractional integration and differentiation of the $(p,q)$--extended modified Bessel function of the second kind and integral transforms

    Purnima Chopra, Mamta Gupta, Kanak Modi

    Abstract : Our aim is to establish certain image formulas of the $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$ by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$. Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erd\'elyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$ and Fox-Wright function $_{r}\Psi_{s}(z)$.

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January, 2024
Vol.39 No.1

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