The reverse order law and the forward have been studied for various types of generalized inverses. $(b,c)$-inverse is a generalization some well known inverses, such as Moore-Penrose inverse, Drazin core etc. In this paper, $(b,c)$-inverse, in unital ring, investigated an equivalent condition to hold derived. Also, results on topic are generalized. Furthermore, ring with unity introduced, diffe...

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

The main purpose of the RESR storage ring in the FAIR project is the accumulation of high intensity antiproton stacks, mainly for the HESR storage ring, but also for the deceleration in the NESR storage ring which provides antiprotons for low energy experiments in the FLAIR experimental area. The high efficiency of antiproton production required for high luminosity experiments in the HESR is ac...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

the zero-divisor graph of a commutative ring r with respect to nilpotent elements is a simple undirected graph $gamma_n^*(r)$ with vertex set z_n(r)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where z_n(r)={x in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...

This paper introduced the use of an adjustable-ring-mode (ARM) laser beam to optimise microstructure and mechanical performance welded 6xxx high-strength aluminium alloy joints. A remote welding system equipped with transverse oscillation was employed parameters, including width core/ring power ratio ARM beam, were investigated sequentially. Results showed that at a constant total has limited c...

The macrocyclic hexanuclear manganese(III) 18-metallacrown-6, [Mn6(pmshz)6(DMF)4(C2H5OH)2]·4DMF (1), where pmshz3− is N-propionyl-N′-5-methylsalicylhydrazide, has been synthesized by self-assembly and structurally characterized. The ring is formed by the succession of six structural moieties of the type [Mn(III)-N-N] with hydrazide N-N groups bridging the ring Mn ions. The ligand enforces the m...