X-Nico

5 unusual facts about Abstract algebra


Arthur Rubin

Rubin's dissertation was entitled Free Algebras in Von Neumann–Bernays–Gödel Set Theory and Positive Elementary Inductions in Reasonable Structures.

Grigore Moisil

He taught the first modern algebra course in Romania, named Logic and theory of proof, at the University of Iaşi.

Narrative

Narratives can be both abstracted and generalised by imposing an algebra upon their structures and thence defining homomorphism between the algebras.

Norman Arthur Wiegmann

Norman Arthur Wiegmann (13 April 1920–14 November 2001) was a mathematician specializing in modern algebra, in particular linear algebra and matrix theory, who spent a major part of his career teaching at the George Washington University and other universities.

Vorlesungen über Zahlentheorie

Dirichlet does not explicitly recognise the concept of the group that is central to modern algebra, but many of his proofs show an implicit understanding of group theory.


Karen Parshall

The subject of her dissertation is the history of the theory of algebras, especially the work of Joseph Wedderburn (The contributions of J. H. M. Wedderburn to the theory of algebras, 1900–1910).

Schanuel's lemma

In mathematics, especially in the area of algebra known as module theory, Schanuel's lemma, named after Stephen Schanuel, allows one to compare how far modules depart from being projective.

Zorn's lemma

It occurs in the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space has a basis, Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that every nonzero ring has a maximal ideal and that every field has an algebraic closure.


see also

Hilbert's theorem

Hilbert's Nullstellensatz, the basis of abstract algebra, establishing a fundamental relationship between geometry and algebra