Abstract
This chapter gives a construction of finite nilmonoids, which is due to the author [1991N], [2001N] and expands earlier ideas of Arendt & Stuth [1970A]; a shorter account is given in Grillet [1995]. Unlike previous constructions for these semigroups, this is a global construction with a very geometric character, in which nilmonoids are obtained as quotient of free commutative monoids by suitable congruences. It accounts well for various structural features of nilmonoids, such as the greatest pure congruence and the universal group of N\0. A more general construction was given by Grillet [2001N] and applied to fully invariant congruences in [2001F].
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© 2001 Springer Science+Business Media Dordrecht
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Grillet, P.A. (2001). Nilsemigroups. In: Commutative Semigroups. Advances in Mathematics, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3389-1_9
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DOI: https://doi.org/10.1007/978-1-4757-3389-1_9
Publisher Name: Springer, Boston, MA
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