Abstract
This chapter contains a global construction of complete group-free semigroups, as quotients of free commutative monoids; finite group-free semigroups are a particular case. This construction bypasses the difficulties, noted earlier, in reassembling archimedean components and Ponizovsky factors, and accounts well for the main structural features of these semigroups (idempotents, ℋ-classes, archimedean components, and Ponizovsky factors); its relation to extension groups will be noted in Chapter XIII. It was first obtained by the author in the case of finite congruences [1993], and generalized to complete group-free congruences in [2001C]. The class of partially free complete semigroups arises as an application.
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© 2001 Springer Science+Business Media Dordrecht
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Grillet, P.A. (2001). Group-Free Semigroups. In: Commutative Semigroups. Advances in Mathematics, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3389-1_10
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DOI: https://doi.org/10.1007/978-1-4757-3389-1_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4857-1
Online ISBN: 978-1-4757-3389-1
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