Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...

Delafossite CuFeO2 hexagonal platelets/rings and graphene composites were synthesized by a low temperature hydrothermal method. The formation mechanism of CuFeO2 hexagonal platelets/rings follows the combined effects of both GO and NaOH. The obtained composites as anode materials display a good battery performance with high reversible capacity, good rate capability and cyclic stability.

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

Let R be a commutative ring with nonzero identity. A proper ideal I of is said to 1-absorbing prime if xyz ∈ for some nonunits x, y, z R, then xy or I. It well known that ⇒ primary semi-primary ideal, is, the class ideals comes between classes and ideals. Also, above right arrows are not reversible. In this article, we characterize rings over which every prime. by comparing other classical such...

We study reversible polymerization of rings. In this stochastic process, two monomers bond and, as a consequence, two disjoint rings may merge into a compound ring or a single ring may split into two fragment rings. This aggregation-fragmentation process exhibits a percolation transition with a finite-ring phase in which all rings have microscopic length and a giant-ring phase where macroscopic...

In this work, we focus on reversible cyclic codes which correspond to reversible DNA codes or reversible-complement DNA codes over a family of finite chain rings, in an effort to extend what was done by Yildiz and Siap in [20]. The ring family that we have considered are of size 2 k , k = 1, 2, · · · and we match each ring element with a DNA 2k−1-mer. We use the so-called u-adic digit system to...

 Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.  The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero  zero-divisors of  $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...