Abstract
The basic algebraic structure that is studied in this chapter is a partial Abelian monoid (PAM in short) (cf. [Wil 1], [Wil 2], [Pul 4], [GuPu]). A PAM is a structure (P; 0, ⊕), where e is a commutative, associative partial binary operation on P and 0 is a neutral element. Beginning with a PAM at the lowest level, we shall consider a hierarchy of partial algebraic structures. The second level is a cancellative PAM (CPAM), the third level is a generalized effect algebra/generalized difference poset, which coincide with a cancellative, positive PAM. Commutative positive minimal clans and BCK-algebras are also included. An effect algebra is a unital generalized effect algebra/D-poset. On higher levels in the hierarchy we find orthoalgebras, orthomodular posets and lattices, MV-algebras, Boolean algebras.
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© 2000 Springer Science+Business Media Dordrecht
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Dvurečenskij, A., Pulmannová, S. (2000). Quotients of Partial Abelian Monoids. In: New Trends in Quantum Structures. Mathematics and Its Applications, vol 516. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2422-7_4
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DOI: https://doi.org/10.1007/978-94-017-2422-7_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5525-5
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