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Ultra deductive systems and (nilpotent) Boolean elements in hoops
- Authors
- Borzooei, R.A.; Jun, Y.B.; Aaly Kologani, M.
- Issue Date
- Feb-2022
- Publisher
- University of Hatef
- Keywords
- Boolean element; Hoop; MV-algebra; nilpotent; ultra deductive system
- Citation
- Journal of Algebraic Hyperstructures and Logical Algebras, v.3, no.1 Special Issue, pp 77 - 93
- Pages
- 17
- Indexed
- SCOPUS
- Journal Title
- Journal of Algebraic Hyperstructures and Logical Algebras
- Volume
- 3
- Number
- 1 Special Issue
- Start Page
- 77
- End Page
- 93
- ISSN
- 2676-6019
- Abstract
- In this paper, first we define the concept of nilpotent element on a hoop H, study some properties of them and investigate the relation with ultra deductive systems. Then by using this notion, we introduce cyclic hoops and prove that every cyclic hoop has a unique generator and is a local MV-algebra. In the follows, we introduce the notion of Boolean elements on hoops and investigate some of their properties and relation among Boolean elements with ultra deductive systems and nilpotent elements. Finally, we introduce a functor between the category of hoops and category of Boolean elements of them. © 2022, University of Hatef. All rights reserved.
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