High Quality Content by WIKIPEDIA articles! In mathematics, dimension theory is a branch of commutative algebra studying the notion of the dimension of a commutative ring, and by extension that of a scheme. The subject, first known as ideal theory, began with Richard Dedekind's work on ideals, itself based on the earlier work of Ernst Kummer and Leopold Kronecker. Later, David Hilbert introduced the term ring to generalize the earlier term number ring. Hilbert introduced a more abstract...
High Quality Content by WIKIPEDIA articles! In mathematics, dimension theory is a branch of commutative algebra studying the notion of the dimension of a commutative ring, and by extension that of a scheme. The subject, first known as ideal theory, began with Richard Dedekind's work on ideals, itself based on the earlier work of Ernst Kummer and Leopold Kronecker. Later, David Hilbert introduced the term ring to generalize the earlier term number ring. Hilbert introduced a more abstract approach to replace the more concrete and computationally oriented methods grounded in such things as complex analysis and classical invariant theory. In turn, Hilbert strongly influenced Emmy Noether, to whom we owe much of the abstract and axiomatic approach to the subject. Another important milestone was the work of Hilbert's student Emanuel Lasker, who introduced primary ideals and proved the first version of the Lasker–Noether theorem.
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