a polynomial   1 2 ( , , , ) n f x x x is called multilinear if it is homogeneous and linear in every one of its variables. in the present paper our objective is to prove the following result: let   r be a prime k-algebra over a commutative ring   k with unity and let 1 2 ( , , , ) n f x x x be a multilinear polynomial over k. suppose that   d is a nonzero derivation on r such that ...

the aim of this paper is to study orders over a valuation ring v with arbitrary rank in acentral simple f-algebra q. the relation between all of the orders is explained with a diagram. it is thenshown that inside bezout order, extremal v-orders are precisely semi-hereditary. in the last section, theeffect of henselization on maximal and semi-hereditary orders is examined.

let $r$ be a commutative ring with identity and $mathbb{a}(r)$ be the set   of ideals of $r$ with non-zero annihilators. in this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $r$, denoted by $mathbb{ag}_p(r)$. it is a (undirected) graph with vertices $mathbb{a}_p(r)=mathbb{a}(r)cap mathbb{p}(r)setminus {(0)}$, where   $mathbb{p}(r)$ is...

this is a survey of some recent applications of abstract algebra, and in particular group rings, to the `communications' areas.

Glucose metabolism via sorbitol pathway has been implicated as a possible contributor to the diabetes-related vascular changes. Nitric oxide plays a major regulatory role in the vascular dilatatory and constricted response. Also it has been observed that diabetes causes vascular changes leading to a decrease in nitric oxide production. Additionally the accumulation of sorbitol is also related t...

It has been shown previously that dendritic branching in cardiorespiratory and locomotor brain areas can be attenuated with exercise training (ET). It was not known whether this process was reversible. Twenty-three (n = 23) male Sprague-Dawley rats were individually caged and divided into two groups: untrained (UN; n = 11) and detrained (DTR; n = 12). DTR were provided with a running wheel at 2...

Nitric oxide (NO) functions as an endothelium-derived relaxing factor by activating guanylate cyclase to increase cGMP levels. However, NO and related species may also regulate vascular tone by cGMP-independent mechanisms. We hypothesized that naturally occurring NO donors could decrease the pulmonary vascular response to serotonin (5-HT) in the intact lung through chemical interactions with 5-...

Nelson, Amanda J., and Gary A. Iwamoto. Reversibility of exercise-induced dendritic attenuation in brain cardiorespiratory and locomotor areas following exercise detraining. J Appl Physiol 101: 1243–1251, 2006. First published June 22, 2006; doi:10.1152/japplphysiol.00483.2006.—It has been shown previously that dendritic branching in cardiorespiratory and locomotor brain areas can be attenuated...

In this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. Next, we investigate some properties of such rings. We prove that $M_n(R)$ is n-f-clean for any n-f-clean ring R. We also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.