Class groups of rank one semisimple monoids

Renner, Lex E.

doi:10.1090/S0002-9939-1988-0938644-5

Class groups of rank one semisimple monoids
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by Lex E. Renner

Proc. Amer. Math. Soc. 103 (1988), 54-58

DOI: https://doi.org/10.1090/S0002-9939-1988-0938644-5

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Abstract:

Let $M$ be an irreducible, normal, algebraic monoid with unit group $S{l_2}\left ( \mathcal {K} \right ) \times {\mathcal {K}^ * },G{l_2}\left ( \mathcal {K} \right )$ or $PG{l_2}\left ( \mathcal {K} \right ) \times {\mathcal {K}^ * }$. In [7] these monoids are classified numerically. In this paper we compute explicitly the divisor class group of each monoid. As a corollary we characterize the monoids with factorial coordinate algebra. All results are independent of the characteristic of $\mathcal {K}$.

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Green’s relations on a connected algebraic monoid

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