Monadic Effect Algebras

Yuxi Zou, Xiaolong Xin and Li Guo

Journal of Mathematics, 2022, vol. 2022, 1-11

Abstract: The main goal of this paper is to introduce and investigate the related theory on monadic effect algebras. First, we design the axiomatic system of existential quantifiers on effect algebras and then use it to give the definition of the universal quantifier and monadic effect algebras. Then, we introduce relatively complete subalgebra and prove that there exists a one-to-one correspondence between the set of all the existential quantifiers and the set of all the relatively complete subalgebras. Moreover, we characterize and give the generated formula of monadic ideals and prove that Riesz monadic ideals and Riesz monadic congruences can be mutually induced. Finally, we study the strong existential quantifier and characterize monadic simple and monadic subdirectly irreducible effect algebras.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2022/6323524.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2022/6323524.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6323524

DOI: 10.1155/2022/6323524

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().