The origin of commutative ring theory in algebraic geometry. (Chinese. English summary) Zbl 1389.13001

Wang, Shuhong

J. Northwest Univ., Nat. Sci. Ed. 47, No. 1, 152-156 (2017).

Summary: As one of the most profound part in abstract algebra, ring theory is an important branch of structural mathematics, which is composed of commutative ring theory and non-commutative ring theory. Commutative ring theory stemmed from algebraic number theory, algebraic geometry and invariant theory in the early 19th century. By the relevant historical material study, the origin of commutative ring theory in algebraic geometry is studied, and the key contributions of Hilbert, Lasker and Macaulay to polynomial ideal theory are deeply analyzed.

MSC:

13-03	History of commutative algebra
01A55	History of mathematics in the 19th century

Keywords:

commutative ring theory; polynomial ideal theory