for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

Let $(R,fm,k)$ be a local Gorenstein ring of dimension $n$. Let $H_{I,J}^i(R)$ be the  local cohomology with respect to a pair of ideals $I,J$ and $c$ be the $inf{i|H_{I,J}^i(R)neq0}$. A pair of ideals $I, J$ is called cohomologically complete intersection if $H_{I,J}^i(R)=0$ for all $ineq c$. It is shown that, when $H_{I,J}^i(R)=0$ for all $ineq c$, (i) a minimal injective resolution of $H_{I,...

In the title compound, C(20)H(19)N(5)O(3)S·H(2)O, the pyrazole ring is connected to a pyrazolone ring, and the two five-membered rings are aligned at 45.0 (1)°. The pyrazole ring is connected to a phenyl ring and the two are twisted by 42.7 (1)°. Finally, the pyrazolone ring is connected to a benzene ring and the two are twisted by 19.5 (1)°. The N-H and -NH(2) portions and the solvent water mo...

‎let $i$ be an ideal in a regular local ring $(r,n)$‎, ‎we will find‎ ‎bounds on the first and the last betti numbers of‎ ‎$(a,m)=(r/i,n/i)$‎. ‎if $a$ is an artinian ring of the embedding‎ ‎codimension $h$‎, ‎$i$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $a$ a {it $t-$extended stretched local ring}‎. ‎this class of‎ ‎local rings is a natural generalization of the class of stretched ...

‎Let $R$ be commutative ring with identity and $M$ be an $R$-module‎. ‎The zero divisor graph of $M$ is denoted $Gamma{(M)}$‎. ‎In this study‎, ‎we are going to generalize the zero divisor graph $Gamma(M)$ to submodule-based zero divisor graph $Gamma(M‎, ‎N)$ by replacing elements whose product is zero with elements whose product is in some submodules $N$ of $M$‎. ‎The main objective of this pa...

In the title mol-ecule, C(15)H(11)N(3), the dihedral angle between the benzene ring and the fused pyrrole ring is 1.07 (5)°. The cyclo-hexene ring adopts an envelope conformation: the dicyano-methyl-ene group at position 1 has a coplanar orientation. An intra-molecular N-H⋯N hydrogen bond generates an S(7) ring motif. Inter-molecular N-H⋯N hydrogen bonds form an R(2) (2)(14) ring in the crystal...

‎In a recent paper C‎. ‎Miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{M}_n(mathbb{R})$ is equal to $4$ if either $n=3$ or $ngeq5$‎. ‎But the case $n=4$ remained open‎, ‎since the diameter could be $4$ or $5$‎. ‎In this work we close the problem showing that also in this case the diameter is $4$.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

a series of ortho -hydroxypyridine-4-ones were prepared in high yields and evaluated for antioxidant and iron chelating activities. n 1 -h hydroxypyridinones va , vb , and ve were the best radical scavengers in dpph free radical scavenging assay. compound vb was proved to be the most potent compound in hydrogen peroxide scavenging assay. all of the synthesized compounds had very close chelating...

a group of 1,3-biarylhydrazide derivatives possessing a cox-2 azido pharmacophore at the para- position of the c-1 phenyl ring in conjunction with a n-3 phenyl or substituted-phenyl ring (4-f,4-cl,4-ome) were designed and synthesized based on nucleophilic substitution reaction. a molecular modelling study of these compounds showed that the designed molecules were well bound with the active site...