A non-zero constant Jacobian polynomial map F = (P,Q) : C −→ C 2 has a polynomial inverse if the component P is a simple polynomial, i.e. if, when P extended to a morphism p : X −→ P of a compactification X of C, the restriction of p to each irreducible component C of the compactification divisor D = X −C is either degree 0 or 1.

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

Let f : X → Y be a morphism of smooth varieties. Then we already know that the (higher) pull-back of a quasicoherent sheaf is quasicoherent. Since a pull-back as a D-module and as an O-module are the same (with some shift,) it is still true for a D-module case. (One might doubt it since in each case the category on which Lif∗ is defined is different, but we can compose a forgetful functor D(Mod...

Let $M$ be an $R$-module and $0 neq fin M^*={rm Hom}(M,R)$. We associate an undirected graph $gf$ to $M$ in which non-zero elements $x$ and $y$ of $M$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. Weobserve that over a commutative ring $R$, $gf$ is connected anddiam$(gf)leq 3$. Moreover, if $Gamma (M)$ contains a cycle,then $mbox{gr}(gf)leq 4$. Furthermore if $|gf|geq 1$, then$gf$ is finit...

We present an initial semantics result for typed higher-order syntax based on monads and modules over monads. The notion of module generalizes the substitution structure of monads. For a simply typed binding signature S we define a representation of S to be a monad equipped with a morphism of modules for each of its arities. The monad of abstract syntax of S then is the initial object in the ca...

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with a non-zero identity and $M$ be a graded $R$-module. In this article, we introduce the concept of graded almost semiprime submodules. Also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.

let $g$ be a group with identity $e$. let $r$ be a $g$-graded commutative ring with a non-zero identity and $m$ be a graded $r$-module. in this article, we introduce the concept of graded almost semiprime submodules. also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.

A vibration isolation module with zero-power magnetic suspension is developed to retrofit a passive vibration isolation system to improve the performance against direct disturbance. In the module, the zero-power magnetic suspension mechanism is connected in series with a normal spring through a middle mass. This structure can generate zero compliance to direct disturbance while the transmitted ...

The aim of this paper is to discuss a notion of Zero Module and Zero Dynamics for linear, time-delay systems. The Zero Module in the time-delay framework is defined using the correspondence between time-delay systems and system with coefficients in a ring, so to exploit algebraic and geometric methods. By combining the algebraic notion of Zero Module and the geometric structure of the lattice o...