Year: 2025
Type: article
Abstract: 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 $(L, \sigma)$ be a type I internal state pseudo $KL$- algebra. If $I$ is a state ideal of $(L, \sigma)$, then $\sigma(I)$ is an ideal of $\sigma(L)$. In the end, we investigate relationships between internal states and Bosbach states, Rie\v{c}an states. Let $\sigma$ be an internal state of type I or type II on a bounded pseudo $L$-algebra $L$ preserving $\rightarrow$ and $\rightsquigarrow$ and $s$ is a Bosbach state on $L$, then the mapping $s_{\sigma}: L \rightarrow [0, 1]$ defined by $s_{\sigma}(x) = s(\sigma(x))$ is a Bosbach state on $L$.
Authors: L.L. Cao, X.L. Xin
Institutions: Xi'an Polytechnic University, Northwest University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412832126