Multiplies of lattice implication algebras
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In this paper, we introduced the notion of multiplier in lattice implication algebra, and considered the properties of multipliers in lattice implication algebras. We give a set of conditions which are equivalent to be an identity multiplier. Also, we characterized the fixed set $Fix_f(L)$ and $Ker f$ by multipliers. Moreover, we prove that if $f$ is a multiplier of a lattice implication algebra, every filter $F$ is a $f$-invariant.
Abstract
In this paper, we introduced the notion of multiplier in lattice implication algebra, and considered the properties of multipliers in lattice implication algebras. We give a set of conditions which are equivalent to be an identity multiplier. Also, we characterized the fixed set $Fix_f(L)$ and $Ker f$ by multipliers. Moreover, we prove that if $f$ is a multiplier of a lattice implication algebra, every filter $F$ is a $f$-invariant.
참고문헌 (5)
- Y. Xu, "Lattice implication algebras", J. Southwest Jiaotong Univ, 1, pp.20~27 (1993)
- Y. Xu, "Lattice H implication algebras and lattice implication algebra classes", J. Hebei Mining and Civil Engineering Institute, 3, pp.139~143 (1992)
- Y. Xu, "On filters of lattice implication algebras", J. Fuzzy Math, 1(2), pp.251~260 (1993)
- S. D. Lee, "On derivations of lattice implication algebras", Ars Combinatoria, 108, pp.279~288 (2013)
- Y. H. Yon, "On f-derivations of lattice implication algebras", Ars Combinatoria, 110, pp.205~215 (2013)