Beyond Earthworm: Keeping the Promise

The founding of the Advanced National Seismic System (ANSS) vision was originally presented in U.S. Geological Survey Circular 1188 (U.S. Geological Survey [USGS], 1999), after many years of discussions and workshops, described in detail by Filson and Arabasz (2016). Much has been accomplished in the ensuing two decades. Disparate and sometimes divergent developments that had been previously explored at individual private and public universities were finally centralized with increased efficiency and coherency of effort. The stated mission of the ANSS is to “… provide accurate and timely data and information products for seismic events, including their effects on buildings and structures, employing modern monitoring methods and technologies.” In this article, an approach (xQuake) is proposed that does not interfere in any way with the mission of the National Earthquake Information Center and ANSS but instead restores much of the community focus and international collaboration that has been lost over the past two decades. xQuake uses an executable graph framework in a pipeline architecture; this framework can be seamlessly integrated into current ANSS quake monitoring systems. This new approach incorporates modern approaches to computer analytics, including multitopic Kafka exchange rings, cloud computing, a self-configuring phase associator, and machine learning. The xGraph system is free for noncommercial use, open source, hardware agnostic (Windows, Linux, Mac), with no requirement for commercial datastores.

Symmetries in idempotent factorizations

In analogy to the fact that isomorphic idempotents arise from flipped factorizations, we show that under some weak conditions, partial factorizations of the complement idempotents may also be preserved. Applying these results, we give new characterizations of exchange rings. We also show that the definition of an exchange element is left–right symmetric.

I-Reversible rings

We study rings in which [Formula: see text] nonzero idempotent implies [Formula: see text] is also an idempotent. We call such rings i-reversible. Besides studying the basic properties of i-reversible rings, we characterize i-reversible triangular matrix rings, i-reversible matrix rings over commutative rings and i-reversible exchange rings.

Additive Maps on Units of Rings

Let R be a ring. A map f: R → R is additive if f(a + b) = f(a) + f(b) for all elements a and b of R. Here, a map f: R → R is called unit-additive if f(u + v) = f(u) + f(v) for all units u and v of R. Motivated by a recent result of Xu, Pei and Yi showing that, for any field F, every unit-additive map of (F) is additive for all n ≥ z, this paper is about the question of when every unit-additivemap of a ring is additive. It is proved that every unit-additivemap of a semilocal ring R is additive if and only if either R has no homomorphic image isomorphic to or R/J(R) ≅ with 2 = 0 in R. Consequently, for any semilocal ring R, every unit-additive map of (R) is additive for all n ≥ 2. These results are further extended to rings R such that R/J(R) is a direct product of exchange rings with primitive factors Artinian. A unit-additive map f of a ring R is called unithomomorphic if f(uv) = f(u)f(v) for all units u, v of R. As an application, the question of when every unit-homomorphic map of a ring is an endomorphism is addressed.

NEC rings

A ring R is called NEC if for any a, b ? N(R), ab = ba. The class of NEC rings is a proper generalization of the class of CN rings. First, with the aid of NEC rings, some characterizations of CN rings and reduced rings are given. Next we extend many properties of CN rings to NEC rings such as we show that NEC rings are directly finite and left min-abel; NEC regular ring are strongly regular; a ring R is NEC if and only if every Pierce stalk of R is NEC; Also we discuss some properties of NEC exchange rings; Finally, we give some properities of MP-invertible elements.

On weakly clean and weakly exchange rings having the strong property

We define two classes of rings calling them weakly clean rings and weakly exchange rings both equipped with the strong property. Although the classes of weakly clean rings and weakly exchange rings are different, their two proper subclasses above do coincide. This extends results due to W. Chen (Commun. Algebra, 2006) and Chin-Qua (Acta Math. Hungar., 2011). We also completely characterize strongly invo-regular rings, thus somewhat extending results due to Danchev-McGovern (J. Algebra, 2015). Some other principal results concerning weakly clean and weakly exchange rings are discussed as well.

The Nilpotent Regular Element Problem

We use George Bergman’s recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element x need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent element x are regular.