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Products of idempotents in algebraic monoids

  • Mohan S. Putcha (a1)
Abstract
Abstract

Let M be a reductive algebraic monoid with zero and unit group G. We obtain a description of the submonoid generated by the idempotents of M. In particular, we find necessary and sufficient conditions for M\G to be idempotent generated.

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References
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[1]Bauer C., Triangular monoids (Ph.D. Thesis, North Carolina State University, Raleigh, N.C., 1999).
[2]Clifford A. H. and Preston G. B., The algebraic theory of semigroups, Vol. 1, Math. Surveys 7 (Amer. Math. Soc., Providence, R.I., 1961).
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[8]Putcha M. S., ‘Regular linear algebraic monoids’, Trans. Amer. Math. Soc. 290 (1985), 615626.
[9]Putcha M. S., Linear algebraic monoids, London Math. Soc. Lecture Note Series 133 (Cambridge Univ. Press, Cambridge, 1988).
[10]Putcha M. S., ‘Algebraic monoids whose nonunits are products of idempotents’, Proc. Amer. Math. Soc. 103 (1998), 3840.
[11]Putcha M. S., ‘Conjugacy classes and nilpotent variety of a reductive monoid’, Canadian J. Math. 50 (1998), 829844.
[12]Putcha M. S. and Renner L. E., ‘The system of idempotents and the lattice of J-classes of reductive algebraic monoids’, J. Algebra 116 (1988), 385399.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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