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State L-algebras and derivations of L-algebras

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Abstract

In this paper, we introduce the notion of state operators on L-algebras and investigate some related properties of such operators. Also, we discuss relations between state operators and states on L-algebras. Using state ideals on state L-algebras, we characterize a kind of state L-algebra, which is state simple. Then, we introduce the co-annihilator of a nonempty set X with respect to a state ideal I and study some properties of them. Finally, we study good derivations and some basic properties of them.

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Acknowledgements

The author is extremely grateful to the editor and the referees for their valuable comments and helpful suggestions which help to improve the presentation of this paper. This research is partially supported by National Natural Science Foundation of China (61602372, 61976176, 11971384) and Xi’an Science and Technology Project (2020KJRC0092).

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  1. Department of Mathematics, Xi’an University of Technology, Shaanxi, 710054, Xi’an, People’s Republic of China

    Xiujuan Hua

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  1. Xiujuan Hua
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Correspondence to Xiujuan Hua.

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Hua, X. State L-algebras and derivations of L-algebras. Soft Comput 25, 4201–4212 (2021). https://doi.org/10.1007/s00500-021-05651-2

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