Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123120220101A generalization of Posner's theorem on generalized derivations in rings1916078710.30504/jims.2022.335190.1059ENN. U.RehmanDepartment of Mathematics, Aligarh Muslim University, 202002, Aligarh, India.E. K.SögütcüDepartment of Mathematics, Sivas Cumhuriyet University, Faculty of Science, Sivas, Turkey.0000-0002-8328-4293H. M.AlnoghashiDepartment of Mathematics, Aligarh Muslim University, 202002, Aligarh, India.0000-0003-0253-6573Journal Article20220325 In this paper, we generalize the Posner's theorem on generalized derivations in rings as follows: Let $\mathscr{A}$ be an arbitrary ring, $\mathscr{I}$ a non-zero ideal, $\mathscr{T}$ is a prime ideal of $\mathscr{A}$ such that $\mathscr{T}\subset \mathscr{I},$ and $\psi $ be a non-zero generalized derivation associated with a non-zero derivation $\rho $ of $\mathscr{A}.$ If one of the following conditions is satisfied: (i) $[\psi (x),x]\in \mathscr{T},$ (ii) $[[\psi (x),x],y]\in \mathscr{T},$ (iii) $\overline{[\psi (x),x]}\in \mathscr{Z}(\mathscr{A}/\mathscr{T})$ and (iv) $\overline{[[\psi (x),x],y]}\in \mathscr{Z}(\mathscr{A}/\mathscr{T})$ $\forall $ $x,y\in \mathscr{I},$ then $\rho (\mathscr{A})\subseteq \mathscr{T}$ or $\mathscr{A}/mathscr{T}$ is commutative. At the example, it is given that the hypothesis of the theorems are necessary.https://jims.ims.ir/article_160787_83e824ba9c6c8ed98d6a76610333af8e.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123120220101Centralizer nearrings112116244110.30504/jims.2022.362376.1074ENG. LWallsDepartment of Mathematics
Southeastern Louisiana UniversityJournal Article20220916Suppose that $(G,+)$ is a group (possibly nonabelian) and that $X$ is a submonoid of the monoid of all endomorphisms of $G$ under the operation of composition of functions, $({\rm End}~{G}, \circ)$. We define the $X$-centralizer nearring of $G$ by $X$ by saying that $M_X(G):=\{ f:G \to G \mid f(0_G)=0_G \text{ and } f \circ \alpha=\alpha \circ f \text{ for all } \alpha \in X \}$. This set of functions, $M_X(G)$, is a nearring under the ``usual" operations of function ``addition" and ``composition" of functions. This paper investigates how centralizer nearrings can be defined and investigates their ideals when $X$ is a group of automorphisms.https://jims.ims.ir/article_162441_9d30a58834b5eaeb6a961b5ba7c861ef.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123120220101Hochschild cohomology of Sullivan algebras and mapping spaces between manifolds233216971110.30504/jims.2023.366483.1078ENJ.-B.GatsinziDepartment of Mathematics and Statistical Sciences, Botswana International University of Science and Technology.Journal Article20221020Let $e: N^n \rightarrow M ^m$ be an embedding of closed, oriented manifolds of dimension $n$ and $m$ respectively. We study the relationship between the homology of the free loop space $LM$ on $M$ and of the space $L_NM$ of loops of $M$ based in $N$ and define a shriek map $ H_*(e)_{!}: H_*( LM, \mathbb{Q}) \rightarrow H_*( L_NM, \mathbb{Q})$ using Hochschild cohomology and study its properties. In particular we extend a result of F\'elix on the injectivity of the map induced by $ \aut_1M \rightarrow \map(N, M; f ) $ on rational homotopy groups when $M$ and $N$ have the same dimension and $ f: N\rightarrow M $ is a map of non zero degree.https://jims.ims.ir/article_169711_084b3ab5598089adc10ebd8835f4671b.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123120220101Dichotomy between operators acting on finite and infinite dimensional Hilbert spaces334117189510.30504/jims.2023.392498.1104ENLuisBernal GonzálezDepartamento de Análisis Matem\ático, Facultad de Matemáticas, Instituto de Matemáticas Antonio de Castro Brzezicki, Universidad de Sevilla, Avenida Reina Mercedes, Sevilla, 41080, Spain.M. S.MoslehianDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.0000-0001-7905-528XJ. B.Seoane SepúlvedaInstituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid, 28040, Spain.Journal Article20230410In this expository article, we give several examples showing how drastically different can be the behavior of operators acting on finite versus infinite dimensional Hilbert spaces. This essay is written as in such a friendly-reader to show that the situation in the infinite dimensional setting is trickier than the finite one.https://jims.ims.ir/article_171895_244ff9a14073747fc46bcc414a3bbb36.pdf