\k₀ of semiartinian von Neumann regular rings. Direct\n finiteness versus unit-regularity

2016/05/15 by Giuseppe Baccella, Baccella, Giuseppe, Leonardo Spinosa +1
Mathematics · #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1605.04606

Abstract

If R is a regular and semiartinian ring, it is proved that the following\nconditions are equivalent: (1) R is unit-regular, (2) every factor ring of\nR is directly finite, (3) the abelian group K₀(R) is free and admits a\nbasis which is in a canonical one to one correspondence with a set of\nrepresentatives of simple right R-modules. For the class of semiartinian and\nunit-regular rings the canonical partial order of K₀(R) is investigated and\nthe directed abelian groups which are realizable as K₀(R) of these rings are\nclassified.\n

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