Let $(K,v)$ be a valued field and let $(K^h,v^h)$ the henselization determined by choice of an extension $v$ to algebraic closure $K$. Consider embedding $v(K^*)\hookrightarrow\Lambda$ value group into divisible ordered abelian group. $T(K,\Lambda)$, $T(K^h,\Lambda)$ trees formed all $\Lambda$-valued extensions $v$, $v^h$ polynomial rings $K[x]$, $K^h[x]$, respectively. We show that natural res...

Throughout, all rings are associative with an identity element but not necessarily commutative. During the decade of 1980s, a series of papers appeared in the Canadian Journal of Mathematics [1, 2] that had investigated pairs of commutative rings with the same set of prime ideals. In this paper, we consider some generalizations of that study in the noncommutative setting. Consider the ring R= H...

Objective: This work aimed to describe the trachea of Magellanic Penguin (Spheniscus magellanicus) through descriptive and morphometric approaches. Methods: ten adult male Spheniscus magellanicus were used, which collected, fixed, kept immersed in an aqueous solution 10% formaldehyde. Results: penguin began caudally from cricoid cartilage larynx, represented by 121.3±5.65 cartilaginous rings jo...

Let $V$ be a valuation domain with quotient field $K$. We show how to describe all extensions of $K(X)$ when the $V$-adic completion $\widehat{K}$ is algebraically closed, generalizing similar result obtained by Ostrowski in case one-dimensional domains. This accomplished realizing such means pseudo-monotone sequences, generalization pseudo-convergent sequences introduced Chabert. also that rin...

In a commutative f-ring, an 1-ideal I is called pseudoprime if ab = 0 implies a E I or b E I, and is called square dominated if for every a E I, lal < x2 for some x E A such that x2 E I. Several characterizations of pseudoprime 1-ideals are given in the class of commutative semiprime frings in which minimal prime 1-ideals are square dominated. It is shown that the hypothesis imposed on the f-ri...

The main theorems of this paper give sharp upper bounds for the minimum distances of one-sided ideals in structural matrix rings defined by directed graphs. It is very well known that additional algebraic structure can give advantages for coding applications (see, for example, [8]). Serious attention in the literature has been devoted to considering properties of ideals in various ring construc...

let r be a ring and v be a matrix valuation on r. it is shown that, there exists a correspondence between matrix valuations on r and some special subsets ?(mvpr) of the set of all square matrices over r, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. furthermore, based on malcolmson’s localization, an alternative proof for t...

0 Introduction In this paper we study, for a certain type of topological rings A, the topological space Cont A of all equivalence classes of continuous valuations of A. The space ContA is defined as follows. Let v: A-+Fw{0} be a valuation of A, where F is an ordered multiplicative group generated by im(v)\{0}. On Fw [0} we introduce the topology such that U _~ F ~ {0} is open iff 0 q~ U or {xeF...

Molecular beam epitaxy of InAs/GaAs quantum dots and their subsequent transformation to quantum rings by postepitaxy thermal annealing have been investigated. Photoconductive detectors with multiple quantum ring layers in the active region exhibit dark current density 10−8 A /cm2 at a bias of 2 V at 4.2 K. The rings have a single bound state, and emission of photoexcited carriers gives rise to ...

This paper develops a general factorization theory of transfer matrices for linear systems defined over rings. Restricting the rings to the class of unique factorization domains (UFDs) and introducing a notion of denominator sets and a generalized notion of coprimeness, a coprime factorization 1 ( ) ( ) ( ) H z W z V z − = for the transfer matrix ( ) H z of a system defined over a UFD is develo...