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Self-similar monoids related to Hahn groups

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Abstract

Self-similar monoids arising from a partially ordered set \(\Omega \) are characterized by generators and relations, and put into a one-to-one correspondence with an abelian lattice-ordered group, the restricted Hahn group of \(\Omega ^{\text{ op }}\). The group of left fractions of such a self-similar monoid A is determined and shown to be closely related to non-commutative prime factorization of elements in A. For a well-ordered set \(\Omega \), this prime factorization specializes to the Cantor Normal Form Theorem for ordinals

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Notes

  1. The terminology is apparent when the operation is interpreted as implication, so that 1 stands for logical truth.

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  1. Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, D-70550, Stuttgart, Germany

    Wolfgang Rump

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  1. Wolfgang Rump
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Correspondence to Wolfgang Rump.

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Communicated by Mark V. Lawson.

Dedicated to B. V. M.

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Rump, W. Self-similar monoids related to Hahn groups. Semigroup Forum 104, 448–463 (2022). https://doi.org/10.1007/s00233-022-10267-5

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