The cardinality of maximal nilpotent subsets of nil rings

determination of maximal singularity free zones in the workspace of parallel manipulator

due to the limiting workspace of parallel manipulator and regarding to finding the trajectory planning of singularity free at workspace is difficult, so finding a best solution that can develop a technique to determine the singularity-free zones in the workspace of parallel manipulators is highly important. in this thesis a simple and new technique are presented to determine the maximal singula...

Extensions of Nilpotent P.P. Rings

Nil, nilpotent and PI-algebras

The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in the ring theory (see e.g. [8], [11], [20]). Banach algebras with these properties have been studied considerably less and the existing results are scattered in literature. The only exception is the work of Krupnik [13], where the Gelfand theory of Banach PI-algebras is presented. Howev...

Strongly nil-clean corner rings

We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings‎, ‎then $R/J(R)$ is nil-clean‎. ‎In particular‎, ‎under certain additional circumstances‎, ‎$R$ is also nil-clean‎. ‎These results somewhat improves on achievements due to Diesl in J‎. ‎Algebra (2013) and to Koc{s}an-Wang-Zhou in J‎. ‎Pure Appl‎. ‎Algebra (2016)‎. ‎...

Some problems and results related to nil and graded-nilpotent rings