Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301Conciseness on normal subgroups and new concise words from outer commutator words717719150210.30504/jims.2024.436404.1159ENG. AFernández-AlcoberDepartment of Mathematics, University of the Basque Country UPV/EHU, Bilbao, Spain.M.PintonelloDepartment of Mathematics, University of the Basque Country UPV/EHU, Bilbao, Spain.Journal Article20240118Let $w=w(x_1,\ldots,x_r)$ be an outer commutator word. We show that the word $w(u_1,\ldots,u_r)$ is concise whenever $u_1,\ldots,u_r$ are non-commutator words in disjoint sets of variables. This applies in particular to words of the form $w(x_1^{n_1},\ldots,x_r^{n_r})$, where the $n_i$ are non-zero integers. Our approach is via the study of values of $w$ on normal subgroups, and in this setting, we obtain the following result: if $N_1,\ldots,N_r$ are normal subgroups of a group $G$ and the set of all values $w(g_1,\ldots,g_r)$ with $g_i\in N_i$ is finite, then also the subgroup generated by these values, i.e. $w(N_1,\ldots,N_r)$, is finite.https://jims.ims.ir/article_191502_3adabf739a9c6890dea02c56c524c857.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301Characterization of the structured pseudospectrum in non-Archimedean Banach spaces799319414610.30504/jims.2024.446376.1163ENJ.EttaybDepartment of Mathematics, Sidi Mohamed Ben Abdellah University, Fez, Morocco.Journal Article20240301In this paper, we demonstrate some results on the pseudospectrum of linear operator pencils on non-Archimedean Banach spaces. In particular, we give a relationship between the Fredholm spectrum of a bounded operator pencil $(A,B)$ and the Fredholm spectrum of the pencil $(A^{-1},B^{-1}).$ Also, we establish a characterization of the essential spectrum of operator pencils on non-Archimedean Banach spaces. Furthermore, we introduce and study the structured pseudospectrum of linear operators on non-Archimedean Banach spaces. We prove that the structured pseudospectra associated with various $\varepsilon$ are nested sets and the intersection of all the structured pseudospectra is the spectrum. We establish a characterization of the structured pseudospectrum of bounded linear operators on non-Archimedean Banach spaces. Finally, we characterize the structured essential pseudospectrum of bounded linear operator pencils on non-Archimedean Banach spaces and we give an illustrative example.https://jims.ims.ir/article_194146_09fa647f2fd39990684a6e3f431f80f8.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301Commutativity of prime ring with generalized skew derivations having a Lie-type behaviour9511119658310.30504/jims.2024.443925.1161ENG.ScudoDepartment of Engineering, University of Messina, Messina, Italy.0000-0002-4478-5589Journal Article20240214Let $R$ be a prime ring of characteristic different from $2$ and $3$, $Q_r$ its right Martindale quotient ring and $C$ its the extended centroid. Suppose that $F$ is a non-zero generalized skew derivation of $R$ such that $F([x,y]_k)=[F(x),y]_k+[x,F(y)]_k$ for all $x,y\in R$, with $k>1$ fixed integer. In this paper we will showw that, then $R$ is commutative. $$F([x; y]_k) = [F(x); y]_k + [x; F(y)]_k$$ for all $x, y \in R$, with $k > 1$ fixed integer. Then $R$ is commutative.https://jims.ims.ir/article_196583_4d7d7c7b39ef4713553ea7935fa4605d.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301Decomposition of complete tripartite graphs into triangles and claws11312619660210.30504/jims.2024.417929.1148ENS.PriyadarsiniDepartment of Mathematics, Periyar University, Salem, Tamilnadu, India.A.MuthusamyDepartment of Mathematics, Periyar University, Salem, TamilNadu, India.Journal Article20230925Let $K_{{r},{s},{t}}$ be a complete tripartite graph with $r\leq s \leq t$. Let $C_{k}$ and $S_{k}$ respectively denote a cycle and a star with $k$ edges. In this paper, we show that the necessary and sufficient conditions for the existence of $\left\{pC_{3},qS_{3}\right\}$ -decomposition of $K_{{r},{s},{t}}$ for all possible values of $p,q\geq0$.https://jims.ims.ir/article_196602_2478fd8481799e54298358f14e3b3d44.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301An overview of $z$-ideals and $z^\circ$-ideals12717019851810.30504/jims.2024.419987.1149ENF.AzarpanahDepartment of Mathematics, Shahid Chamran University of AhvazJournal Article20231009Overall, $z$-ideals and $z^\circ$-ideals in $C(X)$, the ring of all real-valued continuous functions on a space $X$, play a crucial role in the ideal structure of the ring, exhibiting connections with prime ideals and offering insights into the interplay between algebraic and topological properties of the space $X$. By exploring their characteristics and relationships with prime ideals, we can better understand the intricate nature of these ideals and their impact on the structure of $C(X)$. Studying $z$-ideals and $z^\circ$-ideals in reduced rings, particularly in $C(X)$, sheds light on the fundamental aspects of ring theory and topology, highlighting the intricate connections between these two fields. A pseudoprime $z$-ideal is prime, and a prime ideal minimal over a $z$-ideal ($z^\circ$-ideal), is also a $z$-ideal ($z^\circ$-ideal). Additionally, the sum of a prime ideal and a $z$-ideal is a prime $z$-ideal, and every $z$-ideal ($z^\circ$-ideal) is an intersection of prime $z$-ideals ($z^\circ$-ideals). Furthermore, every ideal contains the largest $z$-ideal and is included in the smallest $z$-ideal. These properties demonstrate the significance of $z$-ideals and $z^\circ$-ideals in the ideal structure of the ring $C(X)$ and their role in connecting the algebraic and topological properties of the space $X$. By exploring these properties in reduced rings, especially in $C(X)$, we can appreciate the intricate relationship between the algebraic aspects of $C(X)$ and the topological characteristics of $X$. The elegance and effectiveness of $z$-ideals and $z^\circ$-ideals in this context highlight their importance in understanding the intersection of algebra and topology within $C(X)$. The study of $z$-ideals and $z^\circ$-ideals in reduced rings, particularly in $C(X)$, stands out for its elegance and effectiveness in elucidating the ideal structure of the ring $C(X)$. Inasmuch as $z$-ideals and $z^\circ$-ideals are both algebraic and topological objects, they play a crucial role in bridging the gap between the algebraic properties of $C(X)$ and the topological properties of the space $X$. This article aims to compile and explore the properties of $z$-ideals and $z^\circ$-ideals in $C(X)$, emphasizing their significance in understanding the connections between algebraic and topological aspects within this framework.https://jims.ims.ir/article_198518_7e7713a79b0a18f474bf560c3fdc51f1.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301Some results on rough $\mathcal{I}_{2}$-lacunary statistical convergence of complex uncertain sequences17118920168210.30504/jims.2024.457746.1179ENO.KişiDepartment of Mathematics, Faculty of Science, Bartın University, Bartın, Turkey.M.GürdalDepartment of Mathematics, Suleyman Demirel University, 32260, Isparta, Turkey.R.AkbıyıkDepartment of Mathematics, Bartin University, Bartın, Turkey.Journal Article20240515This paper introduces rough I₂-lacunary statistical convergence for complex uncertain double sequences (CUDS), extending concepts of rough convergence, rough lacunary statistical convergence, and rough I₂-convergence. We explore this notion across four aspects of uncertainty: almost surely, measure, mean, and distribution. Additionally, we investigate rough I₂-lacunary statistical convergence in p-distance and metric spaces for CUDS. The study illustrates the interconnectedness of these convergence concepts and offers observations on their relationships.https://jims.ims.ir/article_201682_60e81ff184ab933b44129db9f90a1f51.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301Gevrey regularity on maximally real submanifolds19120420213810.30504/jims.2024.412001.1140ENJ.YesufDepartment of Mathematics, College of Natural and Computational Science, Samara University, Ethiopia.Journal Article20230816The Fourier -Br\'os -Iagolnitzer (FBI) transform is the right tool to characterize microlocal analyticity, microlocal smoothness, and Gevrey regularity. In this paper, we characterize microlocal Gevrey regularity of a distribution on a maximally real submanifold of $\mathbb{C}^m$ using the FBI transform.https://jims.ims.ir/article_202138_7a9b6eaacb9f0b899d9aeb85755ed0b5.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301Analysis of a certain Pseudo $q$-calculus and its applications in integral inequalities20523220270310.30504/jims.2024.455086.1177ENH. FallahAndevariDepartment of
Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran.A.BabakhaniDepartment of
Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran.0000-0002-5342-1322D. S.OliveiraInstitute of Science and Technology, Federal University of São Paulo, Shariati Ave., São José dos Campos–SP, Brazil.Journal Article20240430We define three new operators which, in exceptional cases, are reduced to\linebreak $q$-integral/derivative $q_a$-integral/derivative and ${}^bq$-integral/derivative operators. Fundamental properties emerge among these specific $q$-operators, like fractional calculus. By utilizing these three newly introduced operators, we can prove various inequalities, the most notable of which are the Chebyshev and Hermite-Hadamard types. Consequently, these new operators provide a generalized approach to many problems in classical inequalities using classical fractional calculus.https://jims.ims.ir/article_202703_9bce2de6c7bdf1f46b753d74007f2229.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301A generalization of normal almost contact manifolds23324120872710.30504/jims.2024.435257.1158ENF.MalekFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.0000-0001-6504-4184A.Ghoujaei Bavil OliaeiDepartment of Mathematics, Payam Noor University Tehran, Iran.Journal Article20240111In this article, a new definition, called $ \varphi $-normal, is introduced, which is a generalization of normal condition on almost contact manifolds. Then some examples of $ \varphi $-normal almost contact manifolds that are not normal are presented, and a sufficient and necessary condition for equivalence of these two definitions in 3-dimensional almost contact manifolds is provided. In the end, it is proven that a $ \varphi$-normal contact metric manifold is a Sasakian manifold.https://jims.ims.ir/article_208727_40c0d8b7bbf8d2372a85b4695b1cd0ac.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301An algebraic proof of the classification of five-dimensional nilsolitons24325220780510.30504/jims.2024.463565.1189ENH. R.Salimi MoghaddamDepartment of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan.0000-0001-6112-4259Journal Article20240618In 2002, using a variational method, Lauret classified five-dimensional nilsolitons. In this work, using the algebraic Ricci soliton equation, we obtain the same classification. We show that, among ten classes of five-dimensional connected and simply connected nilmanifolds, seven classes admit the Ricci soliton structure. In any case, the derivation which satisfies the algebraic Ricci soliton equation is computed.https://jims.ims.ir/article_207805_e8f9188db685d751d710fddcd80728ad.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301Inner amenability of certain Lau algebras associated to discrete crossed products25326020968610.30504/jims.2024.470441.1197ENM. R.GhaneiDepartment of Mathematics, Khansar Campus, University of Isfahan, Isfahan, Iran.Journal Article20240729For a discrete group $\Gamma$, a Hopf von Neumann algebra $(\mathfrak{M},\Delta)$ and a $W^*$-dynamical system $(\mathfrak{M},\Gamma,\alpha)$ such that $(\alpha_s\otimes\alpha_s)\circ\Delta=\Delta\circ\alpha_s$, we show that the crossed product $\mathfrak{M}\rtimes_\alpha\Gamma$ with a co-multiplication is a Hopf von Neumann algebra.<br />Furthermore, we prove that the inner amenability of the predual $\mathfrak{M}_*$ is equivalent to the inner amenability of $(\mathfrak{M}\rtimes_\alpha\Gamma)_*$. Finally, we conclude that if the action $\alpha:\Gamma\rightarrow\mathrm{Aut}(\ell^\infty(\Gamma))$ is defined by $\alpha_s(f)(t)=f(s^{-1}ts)$, then the inner amenability of discrete group $\Gamma$ is equivalent to the inner amenability of $(\ell^\infty(\Gamma)\rtimes_\alpha\Gamma)_*$.https://jims.ims.ir/article_209686_12bc1810e92b5c94fc9bacb29e67a6fc.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125220240301On some properties of neutral SFS-spaces26126920980010.30504/jims.2024.480745.1208ENJ. K.SeypullaevDepartment of
Mathematics, Karakalpak State University named after Berdakh, P.O.Box 230112, Nukus, Uzbekistan.0000-0003-2938-2199A. D.ArzievV.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, P.O.Box 100174,
Tashkent, Uzbekistan.0000-0001-6137-6819K.KalenbaevV.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, P.O.Box 100174,
Tashkent, Uzbekistan.0009-0004-9388-3945Journal Article20240928One of the important problems of the operator algebras theory is the geometric characterization of state spaces of operator algebras.
In this regard, in mid-1980s, a paper by Friedman and Russo introduced facially symmetric spaces. The primary aim of this work was to provide the geometric characterization of predual spaces of $JBW^\ast$-triples that possess an algebraic structure. Many of the properties required in these characterizations are natural assumptions for the state spaces of physical systems. Such spaces are considered as a geometric model for the states of quantum mechanics.
In this paper, we show that if any indecomposable geometric tripotent of a neutral strongly facially symmetric space is a minimal geometric tripotent then any extreme point is a norm exposed point. Moreover, in an atomic neutral locally base normed strongly facially symmetric space any extreme point is a norm exposed point. We also prove that every real neutral strongly facially symmetric space with unitary tripotents is finite.https://jims.ims.ir/article_209800_d1c9e2a8f5bfe16c8597281569c5ae68.pdf