caa a22 4500 605470243 CHVBK 20210128100326.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00500-015-1620-x doi (NATIONALLICENCE)springer-10.1007/s00500-015-1620-x On state residuated lattices [Elektronische Daten] [Pengfei He, Xiaolong Xin, Yongwei Yang] In the paper, we introduce the notion of state operators on residuated lattices and investigate some related properties of such operators. Also, we give characterizations of Rl-monoids and Heyting algebras, and discuss relations between state operators and states on residuated lattices. Using state filters on state residuated lattices, we characterize two kinds of state residuated lattices, which are state simple and state local. Moreover, we focus on algebraic structures of the set $$SF[L]$$ S F [ L ] of all state filters on state residuated lattices. We obtain that $$SF[L]$$ S F [ L ] forms a coherent frame and a pseudocomplemented lattice. Then, we introduce the co-annihilator of a nonempty set $$X$$ X with respect to a state filter $$F$$ F and study some properties of them. As applications, we show that if $$F$$ F and $$G$$ G are filters in a residuated lattice, then the co-annihilator of $$G$$ G with respect to $$F$$ F is the relative pseudocomplement of $$G$$ G with respect to $$F$$ F in the lattice $$F[L]$$ F [ L ] of all filters of residuated lattices. Springer-Verlag Berlin Heidelberg, 2015 Residuated lattice nationallicence State operator nationallicence State filter nationallicence Frame nationallicence Co-annihilator nationallicence He Pengfei College of Mathematics, Northwest University, 710127, Xi'an, People's Republic of China aut Xin Xiaolong College of Mathematics, Northwest University, 710127, Xi'an, People's Republic of China aut Yang Yongwei College of Mathematics, Northwest University, 710127, Xi'an, People's Republic of China aut Soft Computing Springer Berlin Heidelberg 19/8(2015-08-01), 2083-2094 1432-7643 19:8<2083 2015 19 500 https://doi.org/10.1007/s00500-015-1620-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-015-1620-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- He Pengfei College of Mathematics, Northwest University, 710127, Xi'an, People's Republic of China aut NATIONALLICENCE 700 1- Xin Xiaolong College of Mathematics, Northwest University, 710127, Xi'an, People's Republic of China aut NATIONALLICENCE 700 1- Yang Yongwei College of Mathematics, Northwest University, 710127, Xi'an, People's Republic of China aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/8(2015-08-01), 2083-2094 1432-7643 19:8<2083 2015 19 500