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Classes of Non-commutative Residuated Structures

  • Lavinia Corina Ciungu
Part of the Springer Monographs in Mathematics book series (SMM)

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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lavinia Corina Ciungu
    • 1
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA

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