نتایج جستجو برای: cleanness
تعداد نتایج: 199 فیلتر نتایج به سال:
Let R be a commutative local ring. It is proved that R is Henselian if and only if each R-algebra which is a direct limit of module finite R-algebras is strongly clean. So, the matrix ring Mn(R) is strongly clean for each integer n > 0 if R is Henselian and we show that the converse holds if either the residue class field of R is algebraically closed or R is an integrally closed domain or R is ...
a ring $r$ is a strongly clean ring if every element in $r$ is the sum of an idempotent and a unit that commutate. we construct some classes of strongly clean rings which have stable range one. it is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.
A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute. By SRC factorization, Borooah, Diesl, and Dorsey [3] completely determined when Mn(R) over a commutative local ring R is strongly clean. We generalize the notion of SRC factorization to commutative rings, prove that commutative n-SRC rings (n ≥ 2) are precisely the commutative local ring...
The density of the aligned single-walled carbon nanotubes (SWNTs) grown on quartz substrates is an important factor for the performance of fabricated electronic devices. It was discovered that the addition of a sulfur-containing compound (thiophene) to the reaction mixture improved the density of SWNTs by a factor of 2 or more, from approximately 2-4 SWNTs/microm to 6-8 SWNTs/microm under simil...
The Multi-DOF forceps manipulator we developed has two additional DOF of bending on the tip of forceps, and provides new surgical fields and techniques for surgeons. The most remarkable characteristics of the prototype described in this paper are: 1) the small diameter and the small radius of curvature of bending; 2) the confirmation of perfect cleanness and sterilization of this manipulator. I...
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