In this paper, we consider the Frobenius pushforward endofunctor F * ${F}_{\ast}$ of bounded derived category finitely generated modules over an $F$ -finite noetherian local ring. We completely determine categorical entropy in sense Dimitrov, Haiden, Katzarkov, and Kontsevich.

Let F be a field and F[x, y] the ring of polynomials in two variables over F. Let f ∈ F[x, y] and consider the residue class ring R := F[x, y]/fF[x, y]. Our first aim is to study digit representations in R, i.e., we ask for which f each element r ∈ R admits a digit representation of the form d0 + d1x + · · · + d`x with digits di ∈ F[y] satisfying degy di < degy f . These digit systems are motiv...

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...

let $m_r$ be a non-zero‎ ‎module and ${mathcal f}‎: ‎sigma[m_r]times sigma[m_r]‎ ‎rightarrow$ mod-$bbb{z}$ a bifunctor‎. ‎the‎ ‎$mathcal{f}$-reversibility of $m$ is defined by ${mathcal‎ ‎f}(x,y)=0 rightarrow {mathcal f}(y,x)=0$ for all non-zero $x,y$‎ ‎in $sigma[m_r]$‎. ‎hom (resp‎. ‎rej)-reversibility of $m$ is‎ ‎characterized in different ways‎. ‎among other things‎, ‎it is shown‎ ‎th...

Let $D$ be a division ring with center $F$, and $G$ subnormal or quasinormal subgroup of $D^*$. We show that if is locally solvable, then contained in $F$.

Let R be a ring with center Z and I a nonzero ideal of R. An additive mapping F : R → R is called a generalized derivation of R if there exists a derivation d : R → R such that F xy F x y xd y for all x, y ∈ R. In the present paper, we prove that if F x, y ± x, y for all x, y ∈ I or F x ◦ y ± x ◦ y for all x, y ∈ I, then the semiprime ring R must contains a nonzero central ideal, provided d I /...

One o f the ma in aims o f [5] is to obta in bounds for asr(A) for var ious classes of noncommuta t i ve rings A; in part icular , they show that: (i) asr(A) ~< 1 + d whenever A is a module finite a lgebra over a commuta t ive Noe ther ian ring R with d im(maxspec R) = d, and (ii) asr(A) = 1 if A is a semi-local ring (see [5], Theorems 3.1 and 2.4], respectively). The a im o f this note is to s...

Let $f : A rightarrow B$ be a ring homomorphism and $J$ an ideal of $B$. In this paper, we give a necessary and sufficient condition for the amalgamated algebra along an ideal $Abowtie^fJ$ to be $J$-Noetherian. Then we give a characterization for pseudo-irreducible ideals of $Abowtie^fJ$, in special cases.

Proper spindle positioning and orientation are essential for accurate mitosis which requires dynamic interactions between microtubule and actin filament (F-actin). Although mounting evidence demonstrates the role of F-actin in cortical cytoskeleton dynamics, it remains elusive as to the structure and function of F-actin-based networks in spindle geometry. Here we showed a ring-like F-actin stru...