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    Dolinka, Igor East, James Evangelou, Athanasios FitzGerald, Des Ham, Nicholas Hyde, James and Loughlin, Nicholas 2015. Enumeration of idempotents in diagram semigroups and algebras. Journal of Combinatorial Theory, Series A, Vol. 131, p. 119.


    Gould, Victoria and Yang, Dandan 2014. Every group is a maximal subgroup of a naturally occurring free idempotent generated semigroup. Semigroup Forum, Vol. 89, Issue. 1, p. 125.


    Huang, Wenxue 2014. Various Forms of Generating Subsemigroups in Algebraic Monoids. Communications in Algebra, Vol. 42, Issue. 9, p. 3833.


    André, Jorge Araújo, João and Konieczny, Janusz 2011. Regular centralizers of idempotent transformations. Semigroup Forum, Vol. 82, Issue. 2, p. 307.


    Brittenham, Mark Margolis, Stuart W. and Meakin, John 2009. Subgroups of free idempotent generated semigroups need not be free. Journal of Algebra, Vol. 321, Issue. 10, p. 3026.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 80, Issue 2
  • April 2006, pp. 193-203

Products of idempotents in algebraic monoids

  • Mohan S. Putcha (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700013070
  • Published online: 01 April 2009
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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[5]T. E. Hall , ‘On regular semigroups’, J. Algebra 24 (1973), 124.

[7]M. S. Putcha , ‘Algebraic monoids with a dense group of units’, Semigroup Forum 28 (1984), 365370.

[8]M. S. Putcha , ‘Regular linear algebraic monoids’, Trans. Amer. Math. Soc. 290 (1985), 615626.

[10]M. S. Putcha , ‘Algebraic monoids whose nonunits are products of idempotents’, Proc. Amer. Math. Soc. 103 (1998), 3840.

[11]M. S. Putcha , ‘Conjugacy classes and nilpotent variety of a reductive monoid’, Canadian J. Math. 50 (1998), 829844.

[12]M. S. Putcha and L. E. Renner , ‘The system of idempotents and the lattice of J-classes of reductive algebraic monoids’, J. Algebra 116 (1988), 385399.

[13]L. E. Renner , ‘Completely regular algebraic monoids’, J. Pure Appl. Algebra 59 (1989), 291298.

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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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