زر اور معاوضۂ زر: سرمایہ دارانہ اور اسلامی نظام معیشت کے تناظر میں تجزیاتی مطالعہ

Money and its Compensation: An Analysis with Respect to Capitalism and Islamic Economic System In trade and commerce, money has remained the backbone of the business and trade. From the beginning to the end, money is an indispensable part of every economic activity. For this importance, money is treated as a factor of production. But the question is what is meant by money and whether the value of money can be recognized as a land, house, shop, car, bungalow and merchandise goods? And then what is the status if it is in the form of interest and it is linked to inflation? The research article underlines the key aspect regarding money and its compensation in the perspective of capitalistic and Islamic economic system. The qualitative and analytical approach was applied in this article. A literature review concluded that time value of money in capitalistic economy is unlimited while the Islamic economic system does not recognize its value in form of interest and with the association of inflation rate. It is recommended that business to be done on a profit and loss basis, rather than on debt and interest and instead of linking money to the inflation rate, alternatives should be proposed, for example if a person wants to take the loan, he should be given what he needs on cost plus profit basis.

Analog of Groebner bases in a polynomial ring with countably infinite indeterminates

In this dissertation we have developed the theory of Sagbi bases and Sagbi Groebner bases in a polynomial ring with countably infinite indeterminates over a field and also explored the behavior of Sagbi Groebner bases for ideals in algebras of polynomial ring with finite indeterminate over a field under (de)homogenization technique. We have discussed that the things work in a same manner for Sagbi Groebner bases as in case of Groebner and Sagbi bases