Classes of Non-commutative Residuated Structures
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.
- 129.Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Elsevier, Amsterdam (2007) Google Scholar
- 178.Iorgulescu, A.: Classes of BCK-algebras—part V. Preprint 5, Institute of Mathematics of the Romanian Academy (2004) Google Scholar