Abstract.
Residuation is the most natural counterpart of multiplication and has been considered over a period of about 80 years in various roles and situations, e.g. as generalised ideal quotient on the one hand, and as generalised implication on the other hand.
In a first part this paper presents a new development from right hoops to ℓ-groups along an inverse interlink. In a second part this article provides a new approach from positive bounded semiclans (pb-semiclans) to ℓ-group cones, on the one hand, and from commutative bricks (alias MV-algebras) to abelian ℓ-group cones, on the other hand, each of them dominated by the strong structural influence of the adopted top element 1.
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Received: February 17, 2008. Revised: August 25, 2008.
Professor Dr. Dr. h.c. Günter Pickert took his doctoral degree when 20 years old under direction of Helmut Hasse at the Georg August Universität Göttingen on February 17, 1938.
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Bosbach, B. Residuation Groupoids – Again. Result. Math. 53, 27–51 (2009). https://doi.org/10.1007/s00025-008-0329-x
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DOI: https://doi.org/10.1007/s00025-008-0329-x