Communications of the
Korean Mathematical Society
CKMS

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

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  • 2024-04-30

    When every finitely generated regular ideal is finitely presented

    MOHAMED CHHITI, SALAH EDDINE MAHDOU

    Abstract : In this paper, we introduce a weak version of coherent that we call regular coherent property. A ring is called regular coherent, if every finitely generated regular ideal is finitely presented. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

  • 2024-07-31

    On nonnil-$m$-formally Noetherian rings

    Abdelamir Dabbabi, Ahmed Maatallah

    Abstract : The purpose of this paper is to introduce a new class of rings containing the class of $m$-formally Noetherian rings and contained in the class of nonnil-SFT rings introduced and investigated by Benhissi and Dabbabi in 2023 \cite{Amir}. Let $A$ be a commutative ring with a unit. The ring $A$ is said to be nonnil-$m$-formally Noetherian, where $m\geq 1$ is an integer, if for each increasing sequence of nonnil ideals $(I_n)_{n\geq 0}$ of $A$ the (increasing) sequence $(\sum_{i_1+\cdots+i_m=n}I_{i_1}I_{i_2}\cdots I_{i_m})_{n\geq 0}$ is stationnary. We investigate the nonnil-$m$-formally Noetherian variant of some well known theorems on Noetherian and $m$-formally Noetherian rings. Also we study the transfer of this property to the trivial extension and the amalgamation algebra along an ideal. Among other results, it is shown that $A$ is a nonnil-$m$-formally Noetherian ring if and only if the $m$-power of each nonnil radical ideal is finitely generated. Also, we prove that a flat overring of a nonnil-$m$-formally Noetherian ring is a nonnil-$m$-formally Noetherian. In addition, several characterizations are given. We establish some other results concerning $m$-formally Noetherian rings.

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  • 2023-10-31

    Geometry of generalized Berger-type deformed metric on $B$-manifold

    ABDERRAHIM ZAGANE

    Abstract : Let $(M^{2m},\varphi,g)$ be a $B$-manifold. In this paper, we introduce a new class of metric on $(M^{2m},\varphi,g)$, obtained by a non-conformal deformation of the metric $g$, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on $M$ with respect to a generalized Berger-type deformed metric.

  • 2024-07-31

    The Chow ring of a sequence of point blow-ups

    Daniel Camazón Portela

    Abstract : Given a sequence of point blow-ups of smooth $n-$dimensional projective varieties $Z_{i}$ defined over an algebraically closed field $\mathit{k}$, $Z_{s}\xrightarrow{\pi_{s}} Z_{s-1}\xrightarrow{\pi_{s-1}}\cdot\cdot\cdot\xrightarrow{\pi_{2}} Z_{1}\xrightarrow{\pi_{1}} Z_{0}$, with $Z_{0}\cong\mathbb{P}^{n}$, we give two presentations of the Chow ring $A^{\bullet}(Z_{s})$ of its sky. The first one uses the classes of the total transforms of the exceptional components as generators and the second one uses the classes of the strict transforms ones. We prove that the skies of two sequences of point blow-ups of the same length have isomorphic Chow rings. Finally we give a characterization of the final divisors of a sequence of point blow-ups in terms of some relations defined over the Chow group of zero-cycles $A_{0}(Z_{s})$ of its sky.

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  • 2024-10-31

    Monads on Cartesian products of projective spaces

    Damian Muindi Maingi

    Abstract : In this paper we establish the existence of monads on Cartesian products of projective spaces that inject onto an odd dimensional projective spaces.We first construct monads on $\mathbb{P}^1\times\cdots\times\mathbb{P}^1\times\mathbb{P}^3\times\cdots\times\mathbb{P}^3\times\mathbb{P}^5\times\cdots\times\mathbb{P}^5$,then proceed to prove stability of the kernel bundle associated to the monad and simplicity of the cohomology vector bundle.Lastly we establish the existence of monads on $\mathbb{P}^{a_1}\times\cdots\times\mathbb{P}^{a_n }$, where $a_1<a_2<\cdots<a_n$, alternatingeven and odd or at least $a_i$ $0<i\leq{n}$ is odd.

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  • 2024-01-31

    RNA foldings and stuck knots

    Jose Ceniceros, Mohamed Elhamdadi, Josef Komissar, Hitakshi Lahrani

    Abstract : 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 Nelson

    Abstract : 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.

  • 2024-01-31

    Generalized $\eta$-Ricci solitons on para-Kenmotsu manifolds associated to the Zamkovoy connection

    Shahroud azami

    Abstract : 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.

  • 2023-10-31

    Soliton functions and Ricci curvatures of $D$-homothetically deformed $f$-Kenmotsu almost Riemann solitons

    Urmila Biswas, Avijit Sarkar

    Abstract : The present article contains the study of $D$-homothetically deformed $f$-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.

  • 2023-07-31

    Continuous Welch bounds with applications

    K. MAHESH KRISHNA

    Abstract : Let $(\Omega, \mu)$ be a measure space and $\{\tau_\alpha\}_{\alpha\in \Omega}$ be a normalized continuous Bessel family for a finite dimensional Hilbert space $\mathcal{H}$ of dimension $d$. If the diagonal $\Delta := \{(\alpha, \alpha):\alpha \in \Omega\}$ is measurable in the measure space $\Omega\times \Omega$, then we show that \begin{align*} &\ \sup _{\alpha, \beta \in \Omega, \alpha\neq \beta}|\langle \tau_\alpha, \tau_\beta\rangle |^{2m}\\ \geq&\ \frac{1}{(\mu\times\mu)((\Omega\times\Omega)\setminus\Delta)}\left[\frac{ \mu(\Omega)^2}{{d+m-1 \choose m}}-(\mu\times\mu)(\Delta)\right],~\quad \forall m \in \mathbb{N}. \end{align*} This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

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January, 2025
Vol.40 No.1

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