فهرست مطالب
Journal of Linear and Topological Algebra
Volume:13 Issue: 1, Winter 2024
- تاریخ انتشار: 1403/03/16
- تعداد عناوین: 5
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Pages 1-12
Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero identity, $S\subseteq h(R)$ a multiplicatively closed subset of $R$ and $M$ be a graded $R$-module. A graded submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ is said to be graded $S$-strongly prime if there exists $s\in S$ such that whenever $((N+Rx_{g}):_{R}M)y_{h}\subseteq N$, then $sx_{g}\in N$ or $sy_{h}\in N$ for all $x_{g},y_{h}\in h(M)$. The aim of this paper is to introduce and investigate some basic properties of the notion of graded $S$-strongly prime submodules, especially in graded multiplication modules. Moreover, we investigate the behaviour of this structure under graded module homomorphisms, localizations of graded modules, quotient graded modules, Cartesian product.
Keywords: Graded S-Prime Submodule, Graded S-Strongly Prime Submodule, Graded Multiplication Module -
Pages 13-18
New norm and numerical radius inequalities for operators on Hilbert space are given. Among other inequalities, we prove that if $ A, B \in B(H) $, then \[\Vert A \Vert - \frac{3 \Vert A-B^* \Vert }{2} \leq \omega\left(\left[\begin{array}{cc} 0 & A \\ B & 0 \end{array}\right]\right).\] Moreover, $\omega(AB) \leq \frac{3}{2} \Vert Im(A) \Vert \Vert B \Vert + D_{B}\; \omega(A) $. In particular, if $ A $ is self-adjointable, then $\omega(AB) \leq D_{B} \Vert A \Vert$, where $D_{B}=\underset{\lambda \in \mathbb{C}}{\mathop{\inf}}\,\left\| B-\lambda I \right\|$.
Keywords: Hilbert Space, Norm Inequality, Numerical Radius, Bounded Linear Operator -
Pages 19-28
The underlying aim of this paper is first to state the cyclicversion of $\mathcal{J}$-integral Banach type contractive mappings introduced by Fallahi, Ghahramani and Soleimani Rad[Integral type contractions in partially ordered metric spaces and best proximity point, Iran. J. Sci. Technol. Trans. Sci. 44 (2020), 177-183] and second to show the existence of best proximity points for such contractive mappings in a metric space with a graph, which can entail a large number of former best proximity point results. One fundamental issue that can be distinguished between this work and previous researches is that it can also involve all of results stated by taking comparable and $\vartheta$-close elements.
Keywords: Graphical Metric Spaces, Best Proximity Point, $, Mathcal{J}$-Quasi-Contraction, Orbitally $, Mathcal{J}$-Continuous -
Pages 29-37
The main goal of this paper is to compare the proof of the existence and uniqueness of fixed points for $\mathcal{T}$-contractive mappings in various metric spaces and different distances regarding some techniques in mathematical analysis. Also, several comparisons to show the efficiency of the obtained result will be considered.
Keywords: $, Mathcal{T}$-Contraction, Fixed Point, $W$-Distance, Cone Metric Space, Mathfrak{C}$-Distance, Partial Order -
Pages 39-47
In this paper, we study some categorical structures of the category $\mathbf{CoarsePro}$, whose objects are coarse proximity spaces and whose morphisms are coarse proximity maps. We investigate the structure of initial, final, embedding and quotient morphisms in the construct $\mathbf{CoarsePro}$. A special attention is paid to investigate quotients by introducing some conditions that they exist. Also, it is shown that bimorphisms are exactly bijective coarse proximity maps, but not isomorphisms. Consequently, $\mathbf{CoarsePro}$ is not balanced.
Keywords: Coarse Proximity Space, Coarse Proximity Category, Embedding Morphism, Quotient Morphism, Bimorphism