Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-27T11:02:41.806Z Has data issue: false hasContentIssue false

Products of idempotents in algebraic monoids

Published online by Cambridge University Press:  09 April 2009

Mohan S. Putcha
Affiliation:
Department of Mathematics, Box 8205North Carolina State University, Raleigh, NC 27695–8205, USA, e-mail: putcha@math.ncsu.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Bauer, C., Triangular monoids (Ph.D. Thesis, North Carolina State University, Raleigh, N.C., 1999).Google Scholar
[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).Google Scholar
[3]Erdos, J. A., ‘On products of idempotent matrices’, Glasgow Math. J. 8 (1967), 118122.Google Scholar
[4]Fitz-Gerald, D. G., ‘On inverses of products of idempotent in regular semigroups’, J. Austral. Math. Soc. 13 (1972), 335337.Google Scholar
[5]Hall, T. E., ‘On regular semigroups’, J. Algebra 24 (1973), 124.Google Scholar
[6]Howie, J., ‘The semigroup generated by idempotents of a full transformation semigroup’, J. London Math. Soc. 41 (1996), 707716.Google Scholar
[7]Putcha, M. S., ‘Algebraic monoids with a dense group of units’, Semigroup Forum 28 (1984), 365370.Google Scholar
[8]Putcha, M. S., ‘Regular linear algebraic monoids’, Trans. Amer. Math. Soc. 290 (1985), 615626.Google Scholar
[9]Putcha, M. S., Linear algebraic monoids, London Math. Soc. Lecture Note Series 133 (Cambridge Univ. Press, Cambridge, 1988).Google Scholar
[10]Putcha, M. S., ‘Algebraic monoids whose nonunits are products of idempotents’, Proc. Amer. Math. Soc. 103 (1998), 3840.Google Scholar
[11]Putcha, M. S., ‘Conjugacy classes and nilpotent variety of a reductive monoid’, Canadian J. Math. 50 (1998), 829844.Google Scholar
[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.Google Scholar
[13]Renner, L. E., ‘Completely regular algebraic monoids’, J. Pure Appl. Algebra 59 (1989), 291298.Google Scholar