Abstract
In this chapter we study special classes of non-commutative residuated structures: local, perfect and Archimedean structures. The local bounded pseudo-BCK(pP) algebras are characterized in terms of primary deductive systems, while the perfect pseudo-BCK(pP) algebras are characterized in terms of perfect deductive systems. One of the main results consists of proving that the radical of a bounded pseudo-BCK(pP) algebra is normal. We also prove that any linearly ordered pseudo-BCK(pP) algebra and any locally finite pseudo-BCK(pP) algebra are local. Other results state that any local FL w -algebra and any locally finite FL w -algebra are directly indecomposable. The classes of Archimedean and hyperarchimedean FL w -algebras are introduced and it is proved that any locally finite FL w -algebra is hyperarchimedean and any hyperarchimedean FL w -algebra is Archimedean.
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Ciungu, L.C. (2014). Classes of Non-commutative Residuated Structures. In: Non-commutative Multiple-Valued Logic Algebras. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-01589-7_5
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DOI: https://doi.org/10.1007/978-3-319-01589-7_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01588-0
Online ISBN: 978-3-319-01589-7
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