We introduce the notion of weakly quasi invo-clean rings where every element $ r can be written as r=v+e or r=v-e $, $v\in Qinv(R)$ and e\in Id(R) $. study various properties elements rings. prove that ring R=\prod_{i\in I} R_i all are invo-clean, is if only factors but one invo-clean.

The element $q$ of a ring $R$ is called quasi-idempotent if $q^2=uq$ for some central unit $u$ $R$, or equivalently $q=ue$, where and $e$ an idempotent $R$. In this paper, we define that the almost quasi-clean each sum regular element. Several properties almost-quasi clean rings are investigated. We prove every quasi-continuous nonsingular quasi-clean. Finally, it determined conditions under wh...

water and sediment samples were collected from six different stations, located along the nil river between february and june 2015. concentrations of cadmium, lead, zinc, and copper were determined. the extent of the sediment pollution was assessed, using the multiple pollution indices, namely contamination factor (cf), pollution load index (pli), and the geoaccumulation index (igeo). the result...

Soil salinity reduces soybean growth and yield. The recently identified GmSALT3 (Glycine max salt Tolerance-associated gene on chromosome 3) has the potential to improve soybean yields in salinized conditions. Here we evaluate the impact of GmSALT3 on soybean performance under saline or non-saline conditions. Three sets of near isogenic lines (NILs), with genetic similarity of 95.6-99.3% betwee...

The producing cells of the negative regulator of interleukin-3 (NIL-3) were investigated. The 5-fluorouracil-treated bone marrow cells did not produce NIL-3. The bone marrow cells of stem cell-depleted W/WV mouse did not produce the NIL-3, either. The production of NIL-3 was different among mouse strains. Mice of C3H/HeN, A/J and ICR strains produced NIL-3, but the C57BL/6 mice did not produce ...

We show the nonexistence of deep pockets in a large class of groups, extending a result of Bogopol’skĭi. We then give examples of important groups (namely lattices in Nil and Sol) which have deep pockets.

In this paper, we study the transfer of notion $m$-clean ring (i.e., a in which every element is sum unit and an $m$-potent element) to amalgamated bi-amalgamated rings. We also find many sufficient necessary conditions for m-clean property Received: March 7, 2023Accepted: May 31, 2023

We construct new explicit proper biharmonic functions on the 3-dimensional Thurston geometries Sol, Nil, S̃L2(R), H 2 × R and