substitution of two or four carbon atoms by nitrogen in the corannulene molecule as a carbon nanostructure was done and the obtained structures were optimized at mp2/6-31g(d) level of theory. calculations of the nucleus-independent chemical shift (nics) were performed to analyze the aromaticity of the corannulene rings and its derivatives upon doping with n at b3lyp/6-31g(d) level of theory. re...

An elegant and strong theory on noncommutative Noetherian rings has been developed in several groundbreaking works over the second half of the 20th century following the pioneering research of Alfred Goldie in the 1960s. The theory is still an active research area in Algebra and features many important classes of rings such as matrix rings, polynomial rings, differential operator rings, group r...

‎‎let r be a non-commutative ring with unity‎. ‎the commuting graph‎ ‎of $r$ denoted by $gamma(r)$‎, ‎is a graph with a vertex set‎ ‎$rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if‎ ‎$ab=ba$‎. ‎in this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. it is shown that‎, ‎$gamma(r)$ is the disjoint ...

We study finiteness conditions on large tilting modules over arbitrary rings. We then turn to a hereditary artin algebra R and apply our results to the (infinite dimensional) tilting module L that generates all modules without preprojective direct summands. We show that the behaviour of L over its endomorphism ring determines the representation type of R. A similar result holds true for the (in...

Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In additio...

Let $R\to A$ be a homomorphism of associative rings, and let $(\mathcal F,\mathcal C)$ hereditary complete cotorsion pair in $R\mathsf{-Mod}$. F_A,\mathcal C_A)$ the $A\mathsf{-Mod}$ which $\mathcal F_A$ is class all left $A$-modules whose underlying $R$-modules belong to F$. Assuming that F$-resolution dimension every $R$-module finite F$ preserved by coinduction functor $\operatorname{Hom}_R(...

we investigate the classical h.~zassenhaus conjecture‎ ‎for integral group rings of alternating groups $a_9$ and $a_{10}$ of degree‎ ‎$9$ and $10$‎, ‎respectively‎. ‎as a consequence of our‎ ‎previous results we confirm the prime graph‎ ‎conjecture for integral group rings of $a_n$ for all $n leq 10$‎.

A graph is distance-hereditary if for any pair of vertices, their distance in every connected induced subgraph containing both vertices the same as original graph. The Distance-Hereditary Vertex Deletion problem asks, given a G on n and an integer k, whether there set S at most k such that $$G-S$$ distance-hereditary. This important due to its connection parameter rank-width because graphs are ...

Throughout this paper, the ring R is not necessarily with an identity. We denote the set of all idempotents of R by E(R). Also, for a subset X ⊆ R, we denote the right (resp., left) annihilator of X in R by annr(X) (resp., ann (X)). Now, according to Fraser and Nicholson in [5], we call a ring R a left p.p.-ring, in brevity, l.p.p.-ring, if for all x ∈ R, there exists an idempotent e such that ...