CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS

doi:10.1007/s10473-022-0511-3

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 1902-1920.doi: 10.1007/s10473-022-0511-3

• 论文 • 上一篇

CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS

Wei WANG, Bin ZHAO

School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, China

收稿日期:2021-03-05 修回日期:2022-05-26 发布日期:2022-11-02
通讯作者: Bin Zhao,E-mail:zhaobin@snnu.edu.cn E-mail:zhaobin@snnu.edu.cn
基金资助:
This research was supported by the National Natural Science Foundation of China (11531009).

CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS

Wei WANG, Bin ZHAO

School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, China

Received:2021-03-05 Revised:2022-05-26 Published:2022-11-02
Contact: Bin Zhao,E-mail:zhaobin@snnu.edu.cn E-mail:zhaobin@snnu.edu.cn
Supported by:
This research was supported by the National Natural Science Foundation of China (11531009).

摘要/Abstract

摘要： In the paper, we introduce some of multipliers on residuated lattices and investigate the relations among them. First, basing on the properties of multipliers, we show that the set of all multiplicative multipliers on a residuated lattice A forms a residuated lattice which is isomorphic to A. Second, we prove that the set of all total multipliers on A is a Boolean subalgebra of the residuated lattice (which is constituted by all multiplicative multipliers on A) and is isomorphic to the Boolean center of A. Moreover, by partial multipliers, we study the maximal residuated lattices of quotients for residuated lattices. Finally, we focus on principal implicative multipliers on residuated lattices and obtain that the set of principal implicative multipliers on A is isomorphic to the set of all multiplicative multipliers on A under the opposite (dual) order.

关键词: residuated lattice, multiplier, M-multiplier, PI-multiplier, T-multiplier

Abstract: In the paper, we introduce some of multipliers on residuated lattices and investigate the relations among them. First, basing on the properties of multipliers, we show that the set of all multiplicative multipliers on a residuated lattice A forms a residuated lattice which is isomorphic to A. Second, we prove that the set of all total multipliers on A is a Boolean subalgebra of the residuated lattice (which is constituted by all multiplicative multipliers on A) and is isomorphic to the Boolean center of A. Moreover, by partial multipliers, we study the maximal residuated lattices of quotients for residuated lattices. Finally, we focus on principal implicative multipliers on residuated lattices and obtain that the set of principal implicative multipliers on A is isomorphic to the set of all multiplicative multipliers on A under the opposite (dual) order.

Key words: residuated lattice, multiplier, M-multiplier, PI-multiplier, T-multiplier

中图分类号:

06A15

Wei WANG, Bin ZHAO. CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS[J]. 数学物理学报(英文版), 2022, 42(5): 1902-1920.

Wei WANG, Bin ZHAO. CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS[J]. Acta mathematica scientia,Series B, 2022, 42(5): 1902-1920.

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CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS

CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS

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