in this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. weobserve that over a commutative ring $r$, $bbb{ag}_*(_rm)$ isconnected and diam$bbb{ag}_*(_rm)leq 3$. moreover, if $bbb{ag}_*(_rm)$ contains a cycle, then $mbox{gr}bbb{ag}_*(_rm)leq 4$. also for an $r$-module $m$ with$bbb{a}_*(m)neq s(m)setminus {0}$, $...

An elementary proof is given for Hutchinson’s duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.

Composition of time and space in a unified data framework results into spatio-temporal databases. Spatiotemporal Database Management Systems (STDBMS) are able to process, manage and analyze spatiotemporal data. Spatial TAU 1 (STAU), developed in [Pel02], provides spatio-temporal functionality to Oracle10g Object-Relational Database Management System (ORDBMS). Although STAU is designed in a way ...

BACKGROUND Uridine is a therapy for hereditary orotic aciduria and is being investigated in other disorders caused by mitochondrial dysfunction, including toxicities resulting from treatment with nucleoside reverse transcriptase inhibitors in HIV. Historically, the use of uridine as a therapeutic agent has been limited by poor bioavailability. A food supplement containing nucleosides, Nucleomax...

CP violating dipole moments of leptons vanish at least to three loop order and are estimated to be ( ml Mev )×1.6×10−40 e-cm in the standard model (SM), whereml is the mass of the lepton. However they can receive potentially large contributions in some beyond SM scenarios and this makes them very sensitive probes of new physics. In this article we show that a non universal interaction, involvin...

in this paper we characterize the radical of an arbitrary‎ ‎submodule $n$ of a finitely generated free module $f$ over a‎ ‎commutatitve ring $r$ with identity‎. ‎also we study submodules of‎ ‎$f$ which satisfy the radical formula‎. ‎finally we derive‎ ‎necessary and sufficient conditions for $r$ to be a‎ ‎pr$ddot{mbox{u}}$fer domain‎, ‎in terms of the radical of a‎ ‎cyclic submodule in $rbigopl...

In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...