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2014 States and Measures on Hyper BCK-Algebras
Xiao-Long Xin, Pu Wang
J. Appl. Math. 2014: 1-7 (2014). DOI: 10.1155/2014/397265


We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra (H,,0,e) and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a -compatibled regular congruence relation θ and a θ-compatibled inf-Bosbach state s on (H,,0,e). By inducing an inf-Bosbach state s^ on the quotient structure H / [0]θ, we show that H / [0]θ is a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebra H / Ker(m) by a reflexive hyper BCK-ideal Ker(m). Further, we prove that H / Ker(m) is a bounded commutative BCK-algebra.


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Xiao-Long Xin. Pu Wang. "States and Measures on Hyper BCK-Algebras." J. Appl. Math. 2014 1 - 7, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 1404.06017
MathSciNet: MR3182369
Digital Object Identifier: 10.1155/2014/397265

Rights: Copyright © 2014 Hindawi


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