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ON MINIMALITY IN PSEUDO-BCI-ALGEBRAS

Kim, Young-Hee;So, Keum-Sook

  • Received : 2010.08.19
  • Published : 2012.01.31

Abstract

In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements ($x{\leq}a$ implies x = a) in terms of the binary relation $\leq$ which is reflexive and anti-symmetric 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 $\ast$ and $\circ$ are identical, including the property $0{\circ}(0{\ast}a)$ = a. The condition $0{\ast}(0{\circ}x)=0{\circ}(0{\ast}x)=x$ all $x{\in}X$ defines the class of p-semisimple pseudo-BCK/BCI-algebras($0{\leq}x$ implies x = 0) as an interesting subclass whose further properties are also investigated below.

Keywords

(pseudo-)BCK/BCI-algebra;minimal;p-semisimple

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Cited by

  1. Some properties of pseudo-BCK- and pseudo-BCI-algebras 2016, https://doi.org/10.1016/j.fss.2016.12.014
  2. On pseudo-CI algebras pp.1433-7479, 2018, https://doi.org/10.1007/s00500-018-3428-y
  3. Ideals and congruences in pseudo-BCH algebras vol.69, pp.1, 2019, https://doi.org/10.1515/ms-2017-0199