By Ladoshkin M.V.

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**Extra info for A-modules over A-algebras and Hochschild cohomology for modules over algebras**

**Example text**

I view it from another angle — that it brought about an end to the development of Chinese mathematics that began with the rod numerals. The use of the abacus to shorten the time of calculation necessitated the rote learning of numerous mathematical methods. As a result, the rigorous step by step reasoning so essential to the development of mathematics was discarded, and inevitably, mathematics declined. In the second part of this lecture, I would like to present to you my arguments and supporting evidence regarding my thesis that the numeral system that is universally used today, commonly spoken of as the HinduArabic numeral system, has its genesis in the Chinese rod numeral system.

6 An examination of Sun Zi’s use of large numbers in the text indicates that he also followed the nomenclature of this class of number; the largest number is 4 Qian [ed. 1963, p. 531] was of the opinion that much of the text was written by Zhen Luan in the 6th century AD. 5 Although Xu Yue mentioned the whole set of names from yi, zhao to zai, he only gave the values of each category up to jing. The rest of the values shown in the table are inserted according to his principle. 6 This same class of numbers was quoted by Zhu Shijie in his Suanxue qimeng (Introduction to mathematical studies) (1299).

The splendours of China were a magnet, which drew a continuous stream of foreign visitors to its capital, Chang’an, now Xi’an, which was the largest and most cosmopolitan city in the world. As the Chinese rod numeral system had been in continuous use for almost two thousand years by Chinese astronomers, mathematicians, scholars, court officials, Buddhist monks, traders and others, the methods of calculation were easily available to foreigners eager to learn new ideas and inventions from the Chinese.

### A-modules over A-algebras and Hochschild cohomology for modules over algebras by Ladoshkin M.V.

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