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arXiv · 1605.04606

$\mathbf{k}_0$ of semiartinian von Neumann regular rings. Direct finiteness versus unit-regularity

Giuseppe Baccella·Leonardo Spinosa
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Abstract

If $R$ is a regular and semiartinian ring, it is proved that the following conditions are equivalent: (1) $R$ is unit-regular, (2) every factor ring of $R$ is directly finite, (3) the abelian group $K_0(R)$ is free and admits a basis which is in a canonical one to one correspondence with a set of representatives of simple right $R$-modules. For the class of semiartinian and unit-regular rings the canonical partial order of $K_0(R)$ is investigated and the directed abelian groups which are realizable as $K_0(R)$ of these rings are classified.

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Giuseppe Baccella, Leonardo Spinosa. 2016-07-13. $\mathbf{k}_0$ of semiartinian von Neumann regular rings. Direct finiteness versus unit-regularity. https://arxiv.org/abs/1605.04606

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