Communications of the
Korean Mathematical Society

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

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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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  • 2022-10-31

    Notes on $(LCS)_n$-manifolds satisfying certain conditions

    Shyam Kishor, Pushpendra Verma

    Abstract : The object of the present paper is to study the properties of conharmonically flat $(LCS)_n$-manifold, special weakly Ricci symmetric and generalized Ricci recurrent $(LCS)_n$-manifold. The existence of such a manifold is ensured by non-trivial example.

  • 2022-07-31

    A characterization of finite factorization positive monoids

    Harold Polo

    Abstract : We provide a characterization of the emph{positive monoids} (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

  • 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.

  • 2022-07-31

    Semi-neutral groupoids and $BCK$-algebras

    Hee Sik Kim, Joseph Neggers, Young Joo Seo

    Abstract : In this paper, we introduce the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of $BCK$-algebra using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids.

  • 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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  • 2023-04-30

    Estimates for certain shifted convolution sums involving Hecke eigenvalues

    Guodong Hua

    Abstract : In this paper, we obtain certain estimates for averages of shifted convolution sums involving Hecke eigenvalues of classical holomorphic cusp forms. This generalizes some results of L\"{u} and Wang in this direction.

  • 2023-07-31

    S-coherent property in trivial extension and in amalgamated duplication


    Abstract : Bennis and El Hajoui have defined a (commutative unital) ring $R$ to be $S$-coherent if each finitely generated ideal of $R$ is a $S$-finitely presented $R$-module. Any coherent ring is an $S$-coherent ring. Several examples of $S$-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the $S$-coherent property to trivial ring extensions and amalgamated duplications.

  • 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 Le

    Abstract : 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.

  • 2022-10-31

    On functions starlike with respect to $n$-ply symmetric, conjugate and symmetric conjugate points

    Somya Malik, Vaithiyanathan Ravichandran

    Abstract : For given non-negative real numbers $\alpha_k$ with $ \sum_{k=1}^{m}\alpha_k =1$ and normalized analytic functions $f_k$, $k=1,\dotsc,m$, defined on the open unit disc, let the functions $F$ and $F_n$ be defined by $ F(z):=\sum_{k=1}^{m}\alpha_k f_k (z)$, and $F_{n}(z):=n^{-1}\sum_{j=0}^{n-1} e^{-2j\pi i/n} F(e^{2j\pi i/n} z)$. This paper studies the functions $f_k$ satisfying the subordination $zf'_{k} (z)/F_{n} (z) \prec h(z)$, where the function $h$ is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

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April, 2024
Vol.39 No.2

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