Some Results in Weak Pseudo-Quasi-Wajsberg Algebras

In this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak filte...

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Main Authors:	Wenjun Liu, Wenjuan Chen
Format:	Article
Language:	English
Published:	MDPI AG 2019-03-01
Series:	Symmetry
Subjects:	weak pseudo-quasi-Wajsberg algebras filters weak filters residuated
Online Access:	https://www.mdpi.com/2073-8994/11/4/447

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spelling	doaj-c08c6e05c9174fa795940e2b7b1420932020-11-24T20:54:53ZengMDPI AGSymmetry2073-89942019-03-0111444710.3390/sym11040447sym11040447Some Results in Weak Pseudo-Quasi-Wajsberg AlgebrasWenjun Liu0Wenjuan Chen1School of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, Jinan 250022, ChinaSchool of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, Jinan 250022, ChinaIn this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak filters and right weak filters of a weak PQW-algebra and study related properties of them. We also discuss the relation between normal filters and filter congruences on a weak PQW-algebra. Finally, we characterize the relationship between weak PQW-algebras and some bounded residuated quasi-ordered monoids with supplementary conditions.https://www.mdpi.com/2073-8994/11/4/447weak pseudo-quasi-Wajsberg algebrasfiltersweak filtersresiduated
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Wenjun Liu Wenjuan Chen
spellingShingle	Wenjun Liu Wenjuan Chen Some Results in Weak Pseudo-Quasi-Wajsberg Algebras Symmetry weak pseudo-quasi-Wajsberg algebras filters weak filters residuated
author_facet	Wenjun Liu Wenjuan Chen
author_sort	Wenjun Liu
title	Some Results in Weak Pseudo-Quasi-Wajsberg Algebras
title_short	Some Results in Weak Pseudo-Quasi-Wajsberg Algebras
title_full	Some Results in Weak Pseudo-Quasi-Wajsberg Algebras
title_fullStr	Some Results in Weak Pseudo-Quasi-Wajsberg Algebras
title_full_unstemmed	Some Results in Weak Pseudo-Quasi-Wajsberg Algebras
title_sort	some results in weak pseudo-quasi-wajsberg algebras
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2019-03-01
description	In this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak filters and right weak filters of a weak PQW-algebra and study related properties of them. We also discuss the relation between normal filters and filter congruences on a weak PQW-algebra. Finally, we characterize the relationship between weak PQW-algebras and some bounded residuated quasi-ordered monoids with supplementary conditions.
topic	weak pseudo-quasi-Wajsberg algebras filters weak filters residuated
url	https://www.mdpi.com/2073-8994/11/4/447
work_keys_str_mv	AT wenjunliu someresultsinweakpseudoquasiwajsbergalgebras AT wenjuanchen someresultsinweakpseudoquasiwajsbergalgebras
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Some Results in Weak Pseudo-Quasi-Wajsberg Algebras

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