Wyniki wyszukiwania:

Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ( 33], 34], 9]). A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not ?nite-dimensional ( 8, page 155], 32, page V]). Von Neumann proved ( 32, Theorem 14. 1, page 208], 8, page 162]): Every continuous geometry is isomorphic to the lattice of right ideals of some regular ring. The book of K. R. Goodearl ( 14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ( 27], ...

An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group. Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. However, a general theory of acd groups has been developed and a suitable weakening of isomorphism, Lady's near-isomorphism, has been established as the rightconcept for studying acd groups. A number of important classes of acd groups has been successfully classified. Direct...