Abstract
Hahn’s embedding theorem asserts that linearly ordered abelian groups embed in some lexicographic product of real groups. Hahn’s theorem is generalized to a class of residuated semigroups in this paper, namely, to odd involutive commutative residuated chains which possess only finitely many idempotent elements. To this end, the partial lexicographic product construction is introduced to construct new odd involutive commutative residuated lattices from a pair of odd involutive commutative residuated lattices, and a representation theorem for odd involutive commutative residuated chains which possess only finitely many idempotent elements, by means of linearly ordered abelian groups and the partial lexicographic product construction is presented.
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Open access funding provided by University of Pécs (PTE). We thank the anonymous referee for numerous suggestions concerning the presentation of the paper. The present scientific contribution was supported by the GINOP 2.3.2-15-2016-00022 grant and the Higher Education Institutional Excellence Programme 20765-3/2018/FEKUTSTRAT of the Ministry of Human Capacities in Hungary.
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Jenei, S. The Hahn Embedding Theorem for a Class of Residuated Semigroups. Stud Logica 108, 1161–1206 (2020). https://doi.org/10.1007/s11225-019-09893-y
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DOI: https://doi.org/10.1007/s11225-019-09893-y