let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

This paper presents an experimental comparative study of iron losses obtained by means of the Epstein frame, Ring Core and dynamometer tests with non-oriented electrical steel samples. The comparisons are qualitative and they are intended to show the importance of carrying out other tests to evaluate electrical steels in addition to the standard Epstein frame method. In industry, complex or cos...

A library of forty modified aminoglycosides was prepared in which the configuration and regiochemistry of two or three rings was widely varied. The library was based around three core ring systems: the 2-deoxystreptamine ring system found in the natural products, and both enantiomers of (1R*,2R*,4R*,5R*)-2,5-diamino-cyclohexane-1,4-diol and (1R*,3R*,4R*,6R*)-4,6-diaminocyclohexane-1,3-diol. In ...

in this work, we investigate the transfer of some homological properties from a ring $r$ to its amalgamated duplication along some ideal $i$ of $r$ $rbowtie i$, and then generate new and original families of rings with these properties.

A synthetic strategy for the modeling construction of the highly bridged azatetracyclic ABEF ring system of numerous lycoctonine-type C19-diterpenoid alkaloids bearing a characteristic oxygenated quaternary center at C-7 has been successfully developed. The tetracyclic core was constructed rapidly from a readily prepared 6,7-bicyclic AB ring precursor through a 13-step sequence via an advanced ...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

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 mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...