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...

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $$A $$ be a ring with nonzero identity $$1\ne 0.$$ A proper ideal $$P of is said to if for every nonunits $$x,y,z\in $$0\ne xyz\in P, then $$xy\in P$$ or $$z\in P. In addition give many properties characterizations ideals, we also determine rings which prime. Furthermore, investigate C(X), the continuous...

Chemical reaction networks (CRNs) are directed graphs with reactant or product complexes as vertices, and reactions arcs. A CRN is weakly reversible if each of its connected components strongly connected. Weakly can be considered the most important class networks. Now, stoichiometric subspace a network linear span vectors (i.e., difference between complexes). decomposition independent (incidenc...

Viscous overstability (oscillatory instability) may play an important role in the formation of small scale structure in dense planetary rings such as Saturn's B ring. We investigate the growth and saturation of such modes in local particle simulations. Starting from a hydrodynamic model, we develop a set of ordinary differential equations to model the evolution of the amplitudes of the linearly...

The goal of this paper is to give a definition generalization fuzzy prime $\Gamma $-ideals in $-rings by introducing 2-absorbing and weakly completely commutative their properties. Furthermore, we diagram which transition between definitions $-ring. Finally, introduce quotient $-ring $R$ induced the $-ideal $2$-absorbing