let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

Online social networks such as Twitter and Facebook have become a fixture in the lives of millions of people worldwide. Not only are people communicating with those in their social network, but applications like Twitter allow people to publicly broadcast information relevant to them. For the most part initial weather observations are done automatically, however, some aspects of the weather are ...

The south Indian State of Karnataka, once part of several kingdoms and princely states of repute in the Deccan peninsula, is rich in its historic, cultural and anthropological heritage. The State is the home to 42,48,987 tribal people, of whom 50,870 belong to the primitive group. Although these people represent only 6.95 per cent of the population of the State, there are as many as 50 differen...

more necessary and more and more used.In earlier days and among backward and primitive peoples much opposition is felt, and many of us remember in India about 15 years ago the plague riots and the burning of plague camps and hospitals by the very people for whose good they were intended. In India the people and the educated classes are only slowly emerging from the dark ages as regards sanitati...

THE END OF NATURE DURING THE LONG ECONOMIC BOOM ignited by the robotics revolution of the 2020s, the population became ever more concentrated in wealthy megacities, and vat-grown genetically modified foods became the norm. Most people lost any meaningful connection to nature: Who needs the real thing when you have a computer-generated sensory facsimile, complete with designer drugs to complete ...

jahilid poetry should be known as a pre-islamic life. poem has been illustrator during the life of its people and its surrounding shape. perhaps it could be say atlal discussed in the introduction of pre-islamic odes and according to it, is the most popular topics of jahilid poetry. standing on atlal and desolate land, and weep over them, not limited to the pre-islamic poetry, and the poets of ...

The management of IT carve-out projects is very challenging due to the strict time frame, the severe contractual penalties, the huge number of stakeholders and the various as well as unique IT tasks that have to be conducted. Up to now, there is no instrument for evaluating the readiness of the IT for a carve-out and also not for managing such a project. In order to address this, we develop a m...