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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Class groups of rank one semisimple monoids


Author: Lex E. Renner
Journal: Proc. Amer. Math. Soc. 103 (1988), 54-58
MSC: Primary 20M99; Secondary 14M20
DOI: https://doi.org/10.1090/S0002-9939-1988-0938644-5
MathSciNet review: 938644
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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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DOI: https://doi.org/10.1090/S0002-9939-1988-0938644-5
Article copyright: © Copyright 1988 American Mathematical Society

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