Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125120240101A survey of recent results connected with subnormal subgroups11917970210.30504/jims.2023.407445.1135ENM. R.DixonDepartment of Mathematics, University
of Alabama, Tuscaloosa, AL 35487-0350, U. S. A.M.FerraraDipartimento di Matematica e Fisica, Università degli Studi della Campania ``Luigi Vanvitelli'', viale Lincoln 5, Caserta, Italy.M.TrombettiDipartimento di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia,
I-80126,Napoli, Italy.Journal Article20230717In this paper we give a brief survey of some highlights from the theory of subnormal subgroups and then reveal some recent extensions of this theory due to the current authors and others.https://jims.ims.ir/article_179702_34d8860b44b0c58680b61f9592470203.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125120240101On Infinite direct products of Rings modulo their direct sums213118087810.30504/jims.2023.409975.1138ENE.MomtahanDepartment of Mathematics, Yasouj University, Yaouj, Iran.Journal Article20230803In this article, inspiring with a result due to O.A.S. Karamzadeh, we examine the $\prod_{i\in I} R_i/\oplus_{i\in I} R_i$, where $\{R_i\}_{i\in I}$ is an infinite family of rings. We observe that they are not self-injective on either side. In some important cases they are however $\aleph_0$-self-injective. Along this line, we study the interconnection between regularity(in the sense of von Neumann), injectivity and $\aleph_0$-injectivity.https://jims.ims.ir/article_180878_4fb6455e0132c79627e7ef6606d20016.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125120240101A note on arithmetic-geometric-harmonic mean inequality of several positive operators334318432110.30504/jims.2023.415016.1144ENF.MirzapourDepartment of Mathematics, Faculty of science, University of Zanjan, Zanjan, Iran.0000-0001-7477-6475A.MorassaeiDepartment of Mathematics, Faculty of science, University of Zanjan, Zanjan, IranJournal Article20230905Suppose that $B_1,\cdots,B_m$ are positive operators on a Hilbert space $\mathcal{H}$. In this paper we generalize the weighted arithmetic, geometric and harmonic means as follows:<br /><br />\begin{align*}<br /><br />{\mathbf a_m}(\boldsymbol\kappa;\mathbf{B})&={\mathbf a_2}(k_1,N';B_1,{\mathbf a_{m-1}}(\boldsymbol\kappa';\mathbf{B}'))=\frac{k_1B_1+\cdots+k_mB_m}{N}\\<br /><br />{\mathbf h_m}(\boldsymbol\kappa;\mathbf{B})&={\mathbf h_2}(k_1,N';B_1,{\mathbf h_{m-1}}(\boldsymbol\kappa';\mathbf{B}'))=\left(\frac{k_1B_1^{-1}+\cdots+k_mB_m^{-1}}{N}\right)^{-1}\\<br /><br />{\mathbf g_m}(\boldsymbol\kappa;\mathbf{B})&={\mathbf g_2}(k_1,N';B_1,{\mathbf g_{m-1}}(\boldsymbol\kappa';\mathbf{B}'))<br /><br />\end{align*}<br /><br />where $\boldsymbol\kappa=(k_1,\cdots,k_m), N=k_1+\cdots+k_m, \boldsymbol\kappa'=(k_2,\cdots, k_m)$ and $N'=k_2+\cdots+k_m$. We show that the arithmetic-geometric-harmonic mean inequality holds. Also we investigate nine property of the geometric mean.https://jims.ims.ir/article_184321_3573da7c02b254a2b7901dca40a5cc02.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125120240101The unit group of the group algebra $\mathbb{F}_qD_{36}$455318727210.30504/jims.2024.405833.1131ENR. K.SharmaDepartment of
Mathematics, Indian Institute of Technology Delhi, New Delhi-110016, India.Y.KumarDepartment of
Mathematics, Indian Institute of Technology Delhi, New Delhi-110016, India.Journal Article20230707Abstract. Let p be a prime number and Fq be a finite field having q = pn elements and D36 be the dihedral group of order 36. The unit group U(FqD36), of the group algebra FqD36, has been completely characterized.https://jims.ims.ir/article_187272_5ab5d94df22847e3935c9bd798c70ccf.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125120240101Tsallis relative operator entropy properties with some weighted metrics556919046110.30504/jims.2024.435111.1157ENEl HilaliA.LAGA-Laboratory, Science Faculty, Ibn Tofail University, Kenitra, MoroccoM.CherguiDepartment of Mathematics, CRMEF-RSK, EREAM Team, LaREAMI-Lab, Kenitra, Morocco0000-0001-8077-2251Journal Article20240111The present work attempts to provide some properties for Tsallis relative operator entropy $T_p(A | B)$, acting on positive definite matrices, with respect to weighted Hellinger and Alpha Procrustes distances. Many localizations of this operator have been determined. In particular, some estimations of the distances between $T_p(A | B)$ and some standard matrix means are outlined.https://jims.ims.ir/article_190461_811dfdb67bb25b831778029b07a9e9f9.pdf