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.
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.
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.
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 $n = 7$.
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.
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.
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.
Abstract : The purpose of this paper is to introduce a new class of rings containing the class of SFT-rings and contained in the class of rings with Noetherian prime spectrum. Let $A$ be a commutative ring with unit and $I$ be an ideal of $A$. We say that $I$ is SFT if there exist an integer $k\geq 1$ and a finitely generated ideal $F\subseteq I$ of $A$ such that $x^k\in F$ for every $x\in I$. The ring $A$ is said to be nonnil-SFT, if each nonnil-ideal (i.e., not contained in the nilradical of $A$) is SFT. We investigate the nonnil-SFT variant of some well known theorems on SFT-rings. Also we study the transfer of this property to Nagata's idealization and the amalgamation algebra along an ideal. Many examples are given. In fact, using the amalgamation construction, we give an infinite family of nonnil-SFT rings which are not SFT.
Abstract : In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan--Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with $g$ satisfying some general growth at infinity.
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.
Ismael Akray, Amin Mahamad Zebari
Commun. Korean Math. Soc. 2023; 38(1): 21-38
https://doi.org/10.4134/CKMS.c210349
Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma
Commun. Korean Math. Soc. 2023; 38(1): 205-221
https://doi.org/10.4134/CKMS.c210433
Ioannis Diamantis
Commun. Korean Math. Soc. 2022; 37(4): 1221-1248
https://doi.org/10.4134/CKMS.c210169
Harish Chandra, Anurag Kumar Patel
Commun. Korean Math. Soc. 2023; 38(2): 451-459
https://doi.org/10.4134/CKMS.c220108
Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma
Commun. Korean Math. Soc. 2023; 38(1): 205-221
https://doi.org/10.4134/CKMS.c210433
Ismael Akray, Amin Mahamad Zebari
Commun. Korean Math. Soc. 2023; 38(1): 21-38
https://doi.org/10.4134/CKMS.c210349
Anjan Kumar Bhuniya, Manas Kumbhakar
Commun. Korean Math. Soc. 2023; 38(1): 1-9
https://doi.org/10.4134/CKMS.c210057
Atul Gaur, Rahul Kumar
Commun. Korean Math. Soc. 2023; 38(1): 11-19
https://doi.org/10.4134/CKMS.c210272
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