Internal states on pseudo L-algebras

In this paper we introduces internal states on pseudo L-algebras. Firstly, we introduce the notions of internal states of type I and type II on pseudo L-algebras, and we also investigate the properties of internal states. Nextly, we study state ideals on internal states pseudo L-algebra of type I (type II). Let (L, σ) be a type I internal state pseudo $KL$- algebra. If I is a state ideal of (L, σ), then σ(I) is an ideal of σ(L). In the end, we investigate relationships between internal states and Bosbach states, Rie{c}an states. Let σ be an internal state of type I or type II on a bounded pseudo L-algebra L preserving → and and s is a Bosbach state on L, then the mapping sσ: L → [0, 1] defined by sσ(x) = s(σ(x)) is a Bosbach state on L.