1. States on Residuated Skew Lattices
- Author
-
A. Borumand Saeid and R. Koohnavard
- Subjects
Pure mathematics ,High Energy Physics::Lattice ,Applied Mathematics ,010102 general mathematics ,Skew ,02 engineering and technology ,State (functional analysis) ,01 natural sciences ,Computer Science Applications ,Human-Computer Interaction ,Computational Mathematics ,Computational Theory and Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0101 mathematics ,Mathematics - Abstract
In this paper, we introduce the notion of states and state operators on residuated skew lattices and investigate some related properties of them. The relationships between state operators and states on residuated skew lattices are discussed. We prove that every Bosbach state on a residuated skew lattice is a Riecan state and with an example we show that there is a Riecan state on a residuated skew lattice which is not a Bosbach state. Also, some conditions are given for a Riecan state on residuated skew lattice to be a Bosbach state. We present different types of state residuated skew lattices, like weak, strong, simple, local and state-morphism residuated skew lattices. Any weak state-morphism residuated skew lattice is a strong state residuated skew lattice and converse is true under an extra condition.
- Published
- 2021