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Licensed Unlicensed Requires Authentication Published by De Gruyter February 28, 2017

State hoops

Rajab Ali Borzooei, Mona Aaly Kologani and Omid Zahiri
From the journal Mathematica Slovaca


In this paper, we define the notions of a state ⊔-hoop and a state-morphism ⊔-hoop extending the language of hoop by adding a unary operator and investigate some properties of them. Also, we extend state ⊔-hoop to state hoop and study the relation between state hoops and state BL-algebras, MV-algebras and BCK-algebras.

MSC 2010: Primary 03G25; 06D99

(Communicated by Sylvia Pulmannová)


The authors wish to express their appreciation for several excellent suggestions for improvements in this paper made by the editor and referees.


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Received: 2013-12-9
Accepted: 2015-3-30
Published Online: 2017-2-28
Published in Print: 2017-2-1

© 2017 Mathematical Institute Slovak Academy of Sciences