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A new algorithm for computing idempotents of R-trivial monoids by Nijholt, Eddie; Rink, Bob; Schwenker, Sören is a scholarly article available to read on EtoBox.

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The authors of [Primitive orthogonal idempotents for R-trivial monoids, Journal of Algebra] provide an algorithm for finding a complete system of primitive orthogonal idempotents for CM, where M is any finite R-trivial monoid. Their method relies on a technical result stating that R-trivial monoids are equivalent to so-called weakly ordered monoids. We provide an alternative algorithm, based only on the simple observation that an R-trivial monoid may be realised by upper triangular matrices. This approach is inspired by results in the field of coupled cell network dynamical systems, where L-trivial monoids (the opposite notion) correspond to so-called feed-forward networks. We also show that our algorithm only has to be performed for ZM, after which a complete system of primitive orthogonal idempotents may be obtained for RM, where R is any ring with a known complete system of primitive orthogonal idempotents. In particular, the algorithm works if R is any field.

Author

Nijholt, Eddie; Rink, Bob; Schwenker, Sören

Published

2019

Language

EN