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Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups pp 71–108Cite as

Boolean Inverse Semigroups and Additive Semigroup Homomorphisms

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2188))

Abstract

Tarski investigates in [109] partial commutative monoids constructed from partial bijections on a given set. In Kudryavtseva et al. [71], this study is conveniently formalized in the language of inverse semigroups. Further connections can be found in works on K-theory of rings, such as Ara and Exel [7].

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Notes

  1. 1.

    The right skew join of x and y could of course be defined as , that is, \(y \triangledown x\).

  2. 2.

    Although strictly speaking, the operation symbols should not be denoted the same way as their interpretations (in a given structure), that confusion is widespread and harmless.

  3. 3.

    Often transliterated as “Vagner”.

  4. 4.

    This set can be endowed with a well studied structure of topological groupoid , which will however not be of concern in the present work.

  5. 5.

    In Wagner [112, 113], Zhitomirskiy [126, 127], such semigroups are called antigroups.

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  1. Département de Mathématiques, Université de Caen Normandie, Caen, France

    Friedrich Wehrung

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Wehrung, F. (2017). Boolean Inverse Semigroups and Additive Semigroup Homomorphisms. In: Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups. Lecture Notes in Mathematics, vol 2188. Springer, Cham. https://doi.org/10.1007/978-3-319-61599-8_3

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