The group of quotients of the semigroup of invertible nonnegative matrices over local rings

V. V. Nemiro

Moscow State University, Moscow, Russia

Abstract: In this paper, we prove that for a linearly ordered local ring $R$ with $1/2$ the group of quotients of the semigroup of invertible nonnegative matrices $\mathrm G_n(R)$ for $n \geq 3$ coincides with the group $\mathrm{GL}_n(R)$.

UDC: 512.534.7+512.555

 English version: Journal of Mathematical Sciences (New York), 2021, 257:6, 860–875