The unit groups of affine algebraic monoids

Author:
William C. Waterhouse

Journal:
Proc. Amer. Math. Soc. **85** (1982), 506-508

MSC:
Primary 20G15; Secondary 20M10

DOI:
https://doi.org/10.1090/S0002-9939-1982-0660591-1

MathSciNet review:
660591

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Abstract: An affine algebraic group can be embedded as a proper dense subgroup of an affine algebraic monoid iff it has a homomorphism onto the multiplicative group.

**[1]**M. Demazure and P. Gabriel,*Groupes algébriques*. I, North-Holland, Amsterdam, 1970. MR**0302656 (46:1800)****[2]**J. Humphreys,*Linear algebraic groups*, Springer-Verlag, New York, 1975. MR**0396773 (53:633)****[3]**M. S. Putcha,*On linear algebraic semigroups*, Trans. Amer. Math. Soc.**259**(1980), 457-469. MR**567091 (81i:20087)****[4]**-,*On linear algebraic semigroups*. II, Trans. Amer. Math. Soc.**259**(1980), 471-491.**[5]**-,*On linear algebraic semigroups*. III, Internat. J. Math. Math. Sci.**4**(1981), 667-690. MR**663652 (83k:20073a)****[6]**-,*Green's relations on a connected algebraic monoid*(to appear).**[7]**-,*The group of units of a connected algebraic monoid*(to appear).**[8]**-,*Connected algebraic monoids*(to appear).

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DOI:
https://doi.org/10.1090/S0002-9939-1982-0660591-1

Article copyright:
© Copyright 1982
American Mathematical Society