We study central extensions of division rings with orderings of higher level. We show that orderings extend to certain immediate and inert extensions. Further, it is proved that any n–ordered division ring can be extended to a n–ordered division ring with almost real closed center. In the last section an old theorem due to Neumann is generalized: every n–ordered division ring can be extended to...

We study the dynamics of unidirectionally delay-coupled nonlinear oscillators. Cascading them within a ring of fixed total propagation delay, we demonstrate simple scaling behavior of correlation properties. In fact, the correlation properties of a ring with N elements can be deduced from the autocorrelation of the single delayed feedback system. Coupling a ring element to a chain of unidirecti...

In [2], [3], S. Gersten has introduced higher i£-groups of a ring which satisfy properties analogous to those of a generalized homology theory in a suitably defined homotopy category of rings [ l ] . In this announcement we use Gersten's i£-groups to define for a ring R a generalized cohomology theory KR( ), analogous to the AtiyahHirzebruch i£-theory, on the category of finite simplicial sets ...

In this paper, we study the monotonicity properties of the generalized elliptic integrals and establish two Hölder mean inequalities for the generalized Grötzsch ring function μa(r) and the generalized Hersch-Pfluger distortion function φa K(r) . Mathematics subject classification (2010): 30C62, 33E05.

An extensive generalized concept of classical ring set forth the notion of a gamma ring theory. As an emerging field of research, the research work of classical ring theory to the gamma ring theory has been drawn interest of many algebraists and prominent mathematicians over the world to determine many basic properties of gamma ring and to enrich the world of algebra. The different researchers ...

In the paper, we extend the definition of generalized derivations to superalgebras and prove that a generalized superderivation g on a prime superalgebra A is represented as g(x) = ax + d(x) for all x ∈ A, where a is an element of Qmr (the maximal right ring of quotients of A) and d is a superderivation on A. Using the result we study two generalized superderivations when their product is also ...

in this paper, we introduce a class of $j$-quasipolar rings. let $r$ be a ring with identity. an element $a$ of a ring $r$ is called {it weakly $j$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $j(r)$ and the ring $r$ is called {it weakly $j$-quasipolar} if every element of $r$ is weakly $j$-quasipolar. we give many characterizations and investiga...

The purpose of this note is to provide for my algebra class a guide to the proof of Cohen's structure theorem for complete local rings as given by Cohen himself, in the original 1946 paper [C]. In spite of more modern and concise treatments by the likes of Nagata and Grothendieck, the original proof is a model of clarity and the entire paper is a commutative algebra masterpiece. First, a few wo...

We study Kloosterman sums in a generalized ring-theoretic context, that of finite commutative Frobenius rings. prove number identities for twisted sums, loosely clustered around moment computations.

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...