Recently, Douglas and Wang proved that for each polynomial q, the submodule [q] of the Bergman module generated by q is essentially normal [9]. Using improved techniques, we show that the Hardy-space analogue of this result holds, and more.

In mormyrid electric fish, sensory signals from electroreceptors are relayed to secondary sensory neurons in a cerebellum-like structure known as the electrosensory lateral line lobe (ELL). Efferent neurons and interneurons of the ELL also receive inputs of central origin, including electric organ corollary discharge signals, via parallel fibers and via fibers from the juxtalobar nucleus. To un...

All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. ...

Let C be an algebraically closed field of positive characteristic p and complete with respect to a non-archimedean absolute value | . | and Λ ⊂ C a discrete Fp-submodule. Suppose there exists an Fp-basis {λ0, λ1, . . .} of Λ such that 0 < |λ0| < |λ1| < · · · and |λi| −→ ∞. For k ∈ N define the meromorphic function Ck,Λ(z) = ∑ λ∈Λ 1 (z − λ)k on C. We show that all the zeroes x of Ck,Λ satisfy (∗...

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.

background: to determine which radiotherapy parameters are associated with the tumor response of locally advanced non-small cell lung cancer (nsclc) patients undergoing concurrent chemoradiotherapy. materials and methods: thirty one patients with iiia/iiib nsclc underwent chemoradiotherapy with a median dose of 63 gy. on our actual treatments, we made radiotherapy planning to cover the planning...