let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

let $r$ be a commutative ring with identity and $m$ be an$r$-module. let $fspec(m)$ denotes the collection of all prime fuzzysubmodules of $m$. in this regards some basic properties of zariskitopology on $fspec(m)$ are investigated. in particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$fspec(m)$ is a $t_0-$spa...

Let K be a finitely generated extension of Q and A a non-zero abelian variety over K. Let K̃ be the algebraic closure of K and Gal(K) = Gal(K̃/K) the absolute Galois group of K equipped with its Haar measure. For each σ ∈ Gal(K) let K̃(σ) be the fixed field of σ in K̃. We prove that for almost all σ ∈ Gal(K) there exist infinitely many prime numbers l such that A has a non-zero K̃(σ)-rational point ...

Let R = Q a2A R a be an innnite product of zero-dimensional chained rings. It is known that R is either zero-dimensional or innnite-dimensional. We prove that a nite-dimensional homomorphic image of R is of dimension at most one. If each R a is a PIR and if R is innnite-dimensional, then R admits one-dimensional homomorphic images. However, without the PIR hypothesis on the rings R a , we prese...

Treatment with recombinant interleukin 2 and lymphokine-activated killer cells (rIL-2/LAK) has produced a clinical antitumor effect in preliminary human trials. The cytokines -y-interferon (Il'V-y), tumor necrosis factor a (TNF-a), and tumor necrosis factor 0 (TNF-/S, lymphotoxin) have potent in vitro antitumor activity and some clinical toxicities similar to interleukin 2 (IL-2)/LAK. This stud...

We compute the topological susceptibility slope $\chi^\prime$, related to second moment of two-point correlator charge density, $2d$ $\mathrm{CP}^{N-1}$ models for $N=5,11,21$ and $31$ from lattice Monte Carlo simulations. Our strategy consists in performing a double limit: first, we take continuum limit $\chi^\prime$ at fixed smoothing radius physical units; then, zero-smoothing-radius limit. ...

We prove a strengthening of Brauer's height zero conjecture for principal 2-blocks with Galois automorphisms. This requires new extension the Itô–Michler theorem prime 2, again close, this time odd primes p $p$ , characterisation -closed groups via decomposition numbers certain characters.

We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose coradicals are isomorphic to dual Radford dimension $4p$ for a prime $p>5$. In particular, we obtain families new examples without the Chevalley property.

For every prime integer p, M. Hochster conjectured the existence of certain p-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prim...