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States on pseudo-BCI algebras

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2017

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Abstract (2. Language): 
In this paper, we discuss the structure of pseudo-BCI algebras and get that any pseudo-BCI algebra is a union of it's branches. We introduce the notion of local bounded pseudo-BCI algebras and study some related properties. Moreover we define two operations A1, A2 in a local bounded pseudo-BCI algebra A and two local operations V1 and V2 in V (a) for a G M (A). We show that in a A1(A2)-commutative local bounded pseudo-BCI algebra A, (V(a), A1, V1)((V(a), A2, V2)) forms a lattice for all a G M (A). We define a Bosbach state on a local bounded pseudo-BCI algebra. Then we give two examples of local bounded pseudo-BCI algebras to show that there is local bounded pseudo-BCI algebras having a Bosbach state but there is some one having no Bosbach states. Moreover we discuss some basic properties about Bosbach states. If s is a Bosbach state of a local bounded pseudo-BCI algebra A, we prove that A/ker(s) is equivalent to an MV-algebra. We also introduce the notion of state-morphisms on local bounded pseudo-BCI algebras and discuss the relations between Bosbach states and state-morphisms. Finally we give some characterization of Bosbach states.
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