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CKMS

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

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  • 2023-07-31

    On nonnil-SFT rings

    Ali Benhissi, Abdelamir Dabbabi

    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.

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  • 2023-01-31

    On lightlike hypersurfaces of cosymplectic space form

    Ejaz Sabir Lone, Pankaj Pandey

    Abstract : The main purpose of this paper is to study the lightlike hypersurface $(M,\bar{g})$ of cosymplectic space form $\bar{M}(c)$. In this paper, we computed the Gauss and Codazzi formulae of $(M,\bar{g})$ of cosymplectic manifold $(\bar{M},g)$. We showed that we can't obtain screen semi-invariant lightlike hypersurface (SCI-LH) of $\bar{M}(c)$ with parallel second fundamental form $h$, parallel screen distribution and $c\neq 0$. We showed that if second fundamental form $h$ and local second fundamental form $B$ are parallel, then $(M,\bar{g})$ is totally geodesic. Finally we showed that if $(M,\bar{g})$ is umbilical, then cosymplectic manifold $(\bar{M},g)$ is flat.

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  • 2023-10-31

    The dimension of the maximal spectrum of some ring extensions

    Rachida EL KHALFAOUI, Najib Mahdou

    Abstract : Let $A$ be a ring and $\mathcal{J} = \{\text{ideals $I$ of $A$} \,|\, J(I) = I\}$. The Krull dimension of $A$, written $\dim A$, is the sup of the lengths of chains of prime ideals of $A$; whereas the dimension of the maximal spectrum, denoted by $\dim_\mathcal{J} A$, is the sup of the lengths of chains of prime ideals from $\mathcal{J}$. Then $\dim_{\mathcal{J}} A\leq \dim A$. In this paper, we will study the dimension of the maximal spectrum of some constructions of rings and we will be interested in the transfer of the property $J$-Noetherian to ring extensions.

  • 2022-04-30

    Almost weakly finite conductor rings and weakly finite conductor rings

    Hanan Choulli, Haitham El Alaoui, Hakima Mouanis

    Abstract : Let $R$ be a commutative ring with identity. We call the ring $R$ to be an almost weakly finite conductor if for any two elements $a$ and $b$ in $R$, there exists a positive integer $n$ such that $a^{n}Rcap b^{n}R$ is finitely generated. In this article, we give some conditions for the trivial ring extensions and the amalgamated algebras to be almost weakly finite conductor rings. We investigate the transfer of these properties to trivial ring extensions and amalgamation of rings. Our results generate examples which enrich the current literature with new families of examples of non-finite conductor weakly finite conductor rings.

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  • 2023-04-30

    Results associated with the Schwarz lemma on the boundary

    B\"{u}lent Nafi \"{O}rnek

    Abstract : In this paper, some estimations will be given for the analytic functions belonging to the class $\mathcal{R}\left( \alpha \right) $. In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function $h(z)$ and the modulus of the angular derivative of the function $\frac{zh^{\prime }(z)}{ h(z)}$, respectively. Also, the relationship between the coefficients of the analytical function $h(z)$ and the derivative mentioned above will be shown.

  • 2023-01-31

    An exponentially fitted method for two parameter singularly perturbed parabolic boundary value problems

    Gemechis File Duressa, Tariku Birabasa Mekonnen

    Abstract : This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

  • 2023-10-31

    On graded $(m, n)$-closed submodules

    Rezvan Varmazyar

    Abstract : Let $A$ be a $G$-graded commutative ring with identity and $M$ a graded $A$-module. Let $m, n$ be positive integers with $m>n$. A proper graded submodule $L$ of $M$ is said to be graded $(m, n)$-closed if $a^{m}_g\cdot x_t\in L$ implies that $a^{n}_g\cdot x_t\in L$, where $a_g\in h(A)$ and $x_t\in h(M)$. The aim of this paper is to explore some basic properties of these class of submodules which are a generalization of graded $(m, n)$-closed ideals. Also, we investigate $GC^{m}_n-rad$ property for graded submodules.

  • 2022-10-31

    Certain image formulas of $(p,\nu)$--extended Gauss' hypergeometric function and related Jacobi transforms

    Purnima Chopra, Mamta Gupta, Kanak Modi

    Abstract : Our aim is to establish certain image formulas of the $ (p,\nu)$--extended Gauss' hypergeometric function $F_{\,p,\nu}(a,b;c;z)$ by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical 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,\nu)$--extended Gauss's hypergeometric function $F_{\,p,\nu}(a,b;c;z)$ and Fox-Wright function $_{r}\Psi_{s}(z)$. We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the $ (p,\nu)$--extended Gauss' hypergeometric function $F_{\,p,\nu}(a,b;c;z)$.

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  • 2022-10-31

    Circle approximation using parametric polynomial curves of high degree in explicit form

    Young Joon Ahn

    Abstract : 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.

  • 2023-07-31

    A note on certain transformation formulas related to Appell, Horn and Kamp\'{e} de F\'{e}riet functions

    Asmaa Orabi Mohammed, Medhat Ahmed Rakha, Arjun K. Rathie

    Abstract : In 2019, Mathur and Solanki \cite{7,8} obtained a few transformation formulas for Appell, Horn and the Kamp\'{e} de F\'{e}riet functions. Unfortunately, some of the results are well-known and very old results in literature while others are erroneous. Thus the aim of this note is to provide the results in corrected forms and some of the results have been written in more compact form.

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January, 2024
Vol.39 No.1

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