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Filter theory of pseudo hoop-algebras. (English) Zbl 1388.06011

Summary: In this paper, by considering the notion of pseudo hoop-algebras, which introduced by G. Georgescu and A. Iorgulescu in [Mult.-Valued Log. 6, No. 1–2, 95–135 (2001; Zbl 1014.06008)] under the name of residuated integral monoids, and pseudo MV-algebras, pseudo Wajsberg-algebras and pseudo-BL algebras arise as particular cases of them, we introduce the notions of some types of filters ((positive) implicative filters, fantastic filters, associative filters) in pseudo hoop-algebras and to investigate their properties. Several characterizations of (positive) implicative, fantastic and associative filters are derived. Finally, the relations among these filters are investigated.

MSC:

06F35 BCK-algebras, BCI-algebras
03G25 Other algebras related to logic

Citations:

Zbl 1014.06008