Search results

...while retaining essential structural aspects of many objects in [[abstract algebra]] and beyond. The ubiquity of groups in numerous areas—both within and outs ...bgroup]]s, [[quotient group]]s and [[simple group]]s. In addition to their abstract properties, group theorists also study the different ways in which a group ...

| known_for = [[Abstract algebra]]<br />[[Theoretical physics]] ...ies of [[ring (mathematics)|rings]], [[field (mathematics)|fields]], and [[algebra over a field|algebras]]. In physics, [[Noether's theorem]] explains the fun ...

...eger]]s and [[polynomial]]s of one variable. This led to modern [[abstract algebra]]ic notions such as [[Euclidean domain]]s. The Euclidean algorithm has been ...eal]] of ''a'' and ''b''. This GCD definition led to the modern [[abstract algebra]]ic concepts of a [[principal ideal]] (an ideal generated by a single eleme ...