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 ...

Modern Algebra Group theory - basic properties, permutation groups, finite Abelian groups, cosets, normal subgroups, homomorphism theorems, representation. Ring theory - integral domains and fields, ...

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 ...

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 ...