n-Fold Heyting, Boolean and pseudo-MV filters in residuated lattices

被引：0

作者：

Rasouli S. ^{[1
]}

Zarin Z. ^{[2
]}

机构：

[1] Department of Mathematics, Persian Gulf University, Bushehr

[2] Department of Mathematics, Shahid Bahonar University, Kerman

来源：

Afrika Matematika | 2018年 / 29卷 / 5-6期

关键词：

n-fold Boolean filter; n-fold Heyting filter; n-fold MV filter; Residuated lattice;

D O I：

10.1007/s13370-018-0592-2

中图分类号：

学科分类号：

摘要：

This paper is devoted to introduce the notions of n-fold left-(right-)Heyting, n-fold left-(right-)Boolean and n-fold left-(right-)MV filters in residuated lattices and to investigate their properties. Several characterizations of these notions are derived. The relations between n-fold left-(right-)Boolean filters and n-fold left-(right-)Heyting filters are investigated and we prove that an n-fold left-(right-)Boolean filter is an n-fold left-(right-)Heyting filter, respectively, and this implication is strict. Also, the relations between n-fold left-(right-)Boolean filters and n-fold left-(right-)MV filters are investigated and we show that a normal n-fold left-(right-)Boolean filter is a normal n-fold left-(right-)MV filter and each n-fold left-(right-)Heyting and n-fold left-(right-)MV filter is an n-fold left-(right-)Boolean filter. © 2018, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.

引用

页码：911 / 928

页数：17

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