Algebra and Number Theory are cornerstones of modern mathematics. At their heart, these fields study the underlying structures governing numbers and abstract entities, ranging from rings, fields, and ...

Group Theory and Ring Theory form two enduring pillars of modern algebra, each offering profound insights into symmetry, structure, and operations. Group Theory focuses on the study of sets equipped ...

Transactions of the American Mathematical Society, Vol. 359, No. 2 (Feb., 2007), pp. 827-857 (31 pages) We discuss some of the basic ideas of Galois theory for commutative S-algebras originally ...

When Albert Einstein wrote an obituary for Emmy Noether in 1935, he described her as a "creative mathematical genius" who – despite "unselfish, significant work over a period of many years" – did not ...