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Displaying similar documents to “Ordering relations admitting automorphisms”

The almost isomorphism relation for simple regular rings.

Pere Ara, Kenneth R. Goodearl (1992)

Publicacions Matemàtiques

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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.

Arens regularity of lattice-ordered rings

Karim Boulabiar, Jamel Jabeur (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This work discusses the problem of Arens regularity of a lattice-ordered ring. In this prospect, a counterexample is furnished to show that without extra conditions, a lattice-ordered ring need not be Arens regular. However, as shown in this paper, it turns out that any f -ring in the sense of Birkhoff and Pierce is Arens regular. This result is then used and extended to the more general setting of almost f -rings introduced again by Birkhoff.