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Quasi-pseudo-hoops: An Extension to Pseudo-hoops
Wenjuan Chen, Zhaoying Chen and Hongkai Wang

In this paper, we introduce the notion of quasi-pseudo-hoops (π‘žπ‘-hoops, for short) as the generalization of pseudo-hoops. First we give some new notions in order to define π‘žπ‘-hoops. We investigate the basic properties of π‘žπ‘-hoops and also prove that any π‘žπ‘-hoop has the Riesz Decomposition Property. Second we discuss filters of π‘žπ‘-hoops and show that there exists a bijective correspondence between normal filters and filter congruences on any π‘žπ‘-hoop. Finally, we introduce and study some subclasses of π‘žπ‘-hoops. The subdirect product decomposition of a bounded π‘žπ‘-hoop is shown. We also present that bounded Wajsberg π‘žπ‘-hoops with additional conditions are equivalent to quasi-pseudo-MV algebras and bounded basic π‘žπ‘-hoops with additional conditions are equivalent to quasi-pseudo-BL algebras.

Keywords: Filters, Pseudo-hoops, Quasi-pseudo-MV algebras, Quasi-pseudo-BL algebras, Quasi-pseudo-hoops

2010 Mathematics Subject Classification: 03G25; 06A75

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