CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS

doi:10.1007/s10473-022-0511-3

Abstract

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

CLC Number:

06A15

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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