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The almost isomorphism relation for simple regular rings.

Pere Ara, Kenneth R. Goodearl (1992)

Publicacions Matemàtiques

A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K. C. O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism between finitely generated projective modules over a simple regular ring.

The Automorphism Group of the Free Algebra of Rank Two

Cohn, P. (2002)

Serdica Mathematical Journal

The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group...

The existence of envelopes

Edgar E. Enochs, Overtoun M. G. Jenda, Jinzhong Xu (1993)

Rendiconti del Seminario Matematico della Università di Padova

The Strong Anick Conjecture is true

Vesselin Drensky, Jie-Tai Yu (2007)

Journal of the European Mathematical Society

Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K x , y , z over a field K of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of K x , y , z . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a...

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