Research Paper Topological groups, Lie groups
1. Continuity of some mappings on a group via semi-regular topology

M. Ram; S. K. Elagan

Volume 10, Issue 03 , Summer 2021, Pages 179-185

  ‎For a given topological space $(X‎, ‎~\Im)$,‎ ‎there is a coarser topology on $X$ which is called the semi-regular topology on $X$ (generated by regularly open subsets) and it is denoted by $\Im^{\delta}$‎. ‎In this paper‎, ‎we study the continuity of the group operation ...  Read More

Research Paper General algebraic systems
2. An algebraic perspective on neutrosophic sets: fields and linear spaces

V. Cetkin; B. Pazar Varol; H. Aygun

Volume 10, Issue 03 , Summer 2021, Pages 187-198

  In this work, we intend to introduce and study another algebraic structure of single-valued neutrosophic sets called neutrosophic field as a continuation of our investigations on neutrosophic algebraic structures. For this goal, we define the concept of neutrosophic fields and observe some of their basic ...  Read More

Research Paper Operator theory
3. A closure operator versus purity

M. Ghorbani

Volume 10, Issue 03 , Summer 2021, Pages 199-203

  ‎Any notion of purity is normally defined in terms of‎ ‎solvability of some set of equations‎. ‎To study mathematical notions‎, ‎such as injectivity‎, ‎tensor products‎, ‎flatness‎, ‎one needs to have some categorical and‎ ‎algebraic ...  Read More

Review paper General topology
4. Projective system of topological quasi modules

S. Jana; S. Mazumder

Volume 10, Issue 03 , Summer 2021, Pages 205-216

  ‎Quasi module is a new algebraic structure‎, ‎based on module‎, ‎which is composed of a semigroup structure and a partial order accompanied with an external ring multiplication‎. ‎We proposed this structure in our paper \cite{qmod} while we were studying the hyperspace $ \com{M}{} ...  Read More

Research Paper Ordinary differential equations
5. The moving frame method and invariant subspace under parametric group actions

Yousef Alipour Fakhri; Yaser Azadi

Volume 10, Issue 03 , Summer 2021, Pages 217-224

  ‎For a given subspace as a solution space of a linear ODE‎, ‎we define a special linear parametric group action and prolong it to the jet bundle‎. ‎We determine these group parameters by moving frame method and prove that these group parameters are the first integrals of the given ...  Read More

Research Paper Group theory
6. The $n^{th}$ commutativity degree of semigroups

M. Ghaneei; M. Azadi

Volume 10, Issue 03 , Summer 2021, Pages 225-233

  ‎For a given positive integer $n$‎, ‎the $n^{th}$ commutativity degree‎ ‎of a finite non-commutative semigroup $S$ is defined to be the‎ ‎probability of choosing a pair $(x,y)$ for $x‎, ‎y \in S$ such‎ ‎that $x^n$ and $y$ commute in $S$‎. ‎If for every ...  Read More

Research Paper Functional analysis
7. A class of (2m-1)-weakly amenable Banach algebras

M. Yegan

Volume 10, Issue 03 , Summer 2021, Pages 234-239

  ‎Let ${\A}$ be a Banach space and ${\lambda}$ be a non-zero fixed element of ${\A}^{\ast}$(dual space of ${\A}$) with non-zero kernel‎. ‎Defining algebra product in $\A$ as $a\cdot b=\lambda(a)b$ for $a,b\in {\A}$‎, ‎we show that ${\A}$ is a $(2m-1)$-weakly amenable Banach algebra ...  Read More