On Minimality in Pseudo-bci-algebras

نویسندگان

  • Young Hee Kim
  • Keum Sook So
  • B. N. Waphare
  • YOUNG HEE KIM
  • KEUM SOOK SO
چکیده

In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements (x ≤ a implies x = a) in terms of the binary relation ≤ which is reflexive and antisymmetric along with several more complicated conditions. Some of the properties of minimal elements obtained bear resemblance to properties of B-algebras in case the algebraic operations ∗ and ◦ are identical, including the property 0◦(0∗a) = a. The condition 0∗(0◦x) = 0◦(0∗x) = x for all x ∈ X defines the class of p-semisimple pseudo-BCK/BCI-algebras (0 ≤ x implies x = 0) as an interesting subclass whose further properties are also investigated below.

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تاریخ انتشار 2012