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Products of idempotents in regular rings

  • K. C. O'Meara (a1)

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The problem of describing the subsemigroup generated by the idempotents in various natural semigroups has received the attention of several semigroup theorists ([1], [2], [3], [5], [7]). However, in those cases where the parent semigroup is in fact the multiplicative semigroup of a natural ring, the known ring structure has not been exploited. When this ring structure is taken into account, proofs can often be streamlined and can lead to more general arguments (such as not requiring that the elements of the semigroup be already transformations of some known structure).

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References

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1.Dawlings, R. J. H., Products of idempotents in the semigroup of singular endomorphisms of a finite-dimensional vector space, Proc. Roy. Soc. Edinburgh Sect. A 91 (1981), 123133.
2.Dawlings, R. J. H., The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space, Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 351360.
3.Erdos, J. A., On products of idempotent matrices, Glasgow Math. J. 8 (1967), 118122.
4.Goodearl, K. R., Von Neumann regular rings (Pitman, 1979).
5.Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, J. London Math. Soc. 41 (1966), 707716.
6.O'Meara, K. C., Right orders in full linear rings, Ph.D. Thesis, University of Canterbury (1971)
7.Reynolds, M. A. and Sullivan, R. P., Products of idempotent linear transformations, Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 123138.

Products of idempotents in regular rings

  • K. C. O'Meara (a1)

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