Monadic Effect Algebras
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 intr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6323524 |
| _version_ | 1811181734077661184 |
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| author | Yuxi Zou Xiaolong Xin |
| author_facet | Yuxi Zou Xiaolong Xin |
| author_sort | Yuxi Zou |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T09:22:26Z |
| format | Article |
| id | doaj.art-4e9a438870cc4723b2faa9f669a25148 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-04-11T09:22:26Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-4e9a438870cc4723b2faa9f669a251482022-12-22T04:32:09ZengHindawi LimitedJournal of Mathematics2314-47852022-01-01202210.1155/2022/6323524Monadic Effect AlgebrasYuxi Zou0Xiaolong Xin1School of Mathematics and StatisticsSchool of ScienceThe 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.http://dx.doi.org/10.1155/2022/6323524 |
| spellingShingle | Yuxi Zou Xiaolong Xin Monadic Effect Algebras Journal of Mathematics |
| title | Monadic Effect Algebras |
| title_full | Monadic Effect Algebras |
| title_fullStr | Monadic Effect Algebras |
| title_full_unstemmed | Monadic Effect Algebras |
| title_short | Monadic Effect Algebras |
| title_sort | monadic effect algebras |
| url | http://dx.doi.org/10.1155/2022/6323524 |
| work_keys_str_mv | AT yuxizou monadiceffectalgebras AT xiaolongxin monadiceffectalgebras |