Almost at the same time of Galois' work, the British mathematician peacock published his General Theory of Algebra (1830), in which he studied the basic laws of algebraic operations and tried to establish a more general algebra, which is just the science of symbols and some algorithms they satisfy. British mathematicians Augustus de Morgan and Bull also made important attempts in this respect. These works foreshadowed the emergence of abstract algebra.

Another book that caused algebraic changes came from British mathematician Hamilton and German mathematician grassmann. The former constructs the first mathematical object-quaternion which does not satisfy the multiplicative commutative law in 1843, while the latter independently obtains a more general theory of n-component hypercomplex in 1844.

In number theory, due to the study of Fermat's last theorem, German mathematician Cuomo introduced the concept of "ideal number" (1845- 1847), and Dai Dejin developed the ideal theory on this basis. This work not only has an important influence on the development of algebraic number theory, but also opens the way for the development of abstract algebra.

Under the influence of Boolean work, British mathematicians Gloria and Sylvester jointly established algebraic theory, which laid the foundation for algebraic invariant theory. This work is also the driving force leading to the establishment of abstract algebra.

Since the19th century, some works have caused changes in algebra, and finally led to the emergence of abstract algebra. These works can be divided into three main aspects: group theory, algebraic number theory and linear algebra. By the end of 19, mathematicians have abstracted their * * * same characteristics from many scattered concrete research objects for axiomatic research, and completed the synthesis of the work from the above three aspects. Algebra has finally turned from equation theory to algebraic operation. Modern German schools have played a major role in this comprehensive work. Starting from the work of Dedeking and Hilbert at the end of 19, under the influence of Weber's three-volume masterpiece, Stanik published his important paper Algebraic Theory of Fields in191year, which made great contributions to the establishment of abstract algebra. Since the 1920s, abstract algebra has made unprecedented progress, mainly focusing on A.E. Nott, Atin, their colleagues and students. Vander Waals Deng, a Dutch mathematician, wrote Modern Algebra in the early 1930s based on the speeches of A.E. Nott and Atin, which integrated all aspects of abstract algebra in one book at that time, and played a great role in promoting the spread and development of abstract algebra.

Abstract algebra focuses on the laws of algebraic operations of numbers, words and more general elements and the properties of various algebraic structures defined by axioms applicable to these operations. Therefore, abstract algebra has an important influence on all modern mathematics and other scientific fields.

With the development and application of various branch theories in mathematics, abstract algebra has been continuously developed. 1933- 1938, through the work of G.D. boekhoff, von Neumann, kantorovich and Si Tong, lattice theory established its position in algebra. Since the mid-1940s, as a generalization of linear algebra, modular theory has been further developed and exerted a far-reaching influence. New branches such as universal algebra, homology algebra and category are also established and developed.

The study of abstract algebra began in the 1930s. Mathematicians in China have made great achievements in many aspects, especially the work of Ceng Jiong Zhi, Hua and Zhou Weiliang.

Now, because of its special importance, algebra has been included in textbooks. As an important subject, it will be studied systematically in universities.