There is no doubt that algebra is developed from arithmetic. As for when algebra came into being, it's hard to say clearly. If you think "algebra" refers to the skills of solving algebraic equations such as bx+k=0. This kind of "algebra" was only developed in the 16th century, the Vedas, the father of French algebra.
If algebraic symbols are not required to be as concise as they are now, then the generation of algebra can be traced back to an earlier era.
Westerners regard Diophantine, an ancient Greek mathematician in the third century BC, as the originator of algebra, and the mathematician who really founded algebra was Muhammad Ibn Moussa (about 780-850 AD). In China, algebraic problems expressed in words appeared earlier.
"Algebra", as a proprietary mathematical term, represents a branch of mathematics. It was officially used in China, and it was first used in 1859. That year, Li, a mathematician in Qing Dynasty, and Leali, an Englishman, translated a book written by Di Yaogan, an Englishman. The name of the translation is algebra. Of course, the contents and methods of algebra have long been produced in ancient China. For example, there are equation problems in "Nine Chapters of Arithmetic".
The origin of algebra can be traced back to the Babylonian era, when people developed a more advanced arithmetic system, which enabled them to calculate by algebraic methods. Through the use of this system, they can list equations with unknowns and solve them. Nowadays these problems are generally solved by linear equations, quadratic equations and indefinite linear equations. In contrast, most Egyptians in this period and most Indian, Greek and China mathematicians in the 1 century BC generally used geometric methods to answer such questions, such as those described in Rand's mathematical cursive book Rope Sutra, Geometry Elements and Nine Chapters of Arithmetic. Greece's work in geometry, taking geometry as a classic, provides a framework and generalizes the formulas for solving specific problems into a more general system for describing and solving algebraic equations.
Algebra comes from the Arabic word "al-jabr", which comes from al-Kitāb al-mu? ta？ ar fī？ isāb al-？ Abr wa-l-muqābala, the title of this book, means the summary of the calculation of shifting terms and merging similar terms, which was written by Musa in 820. The word Al-Jabr means "reunion". Traditionally, Diophantine, a Greek mathematician, was regarded as the "father of algebra", and his achievements are still useful today. He even gave a detailed explanation of solving quadratic equations. Those who support Diophantine think that algebra in Al-Jabr is more basic than arithmetic, and the arithmetic is very simple, while Al-Jabr is completely a literary work. Another Persian mathematician, Omar Khayyam, developed algebraic geometry and found the general geometric solution of cubic equation. Indian mathematicians Mahaviro and Bhashgaro and China mathematician Zhu Shijie have developed many solutions to cubic, quartic, quintic and higher polynomial equations.
Another key event in the further development of algebra lies in the general algebraic solutions of cubic and quartic equations, which developed in the middle of16th century. The concept of determinant was developed by Japanese mathematician Guan Xiaohe in the17th century, and it was further developed by Leibniz ten years later, with the purpose of solving the answers of linear equations with matrices. Gabriel cramer did the same work for matrices and determinants in the18th century. The development of abstract algebra began in the19th century, and at first it mainly focused on the problems called Galois Theory and Rules.