Boolean Algebras with Semigroup Operators: Free Product and Free Objects
Two important algebraic structures are S-acts and Boolean algebras. Combining these two structures, one gets S-Boolean algebras, equipped with a compatible right action of a monoid S which is a special case of Boolean algebras with operators. In this article, we considered some category-theoretic pr...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/3761080 |
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| _version_ | 1849691933299965952 |
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| author | H. Barzegar |
| author_facet | H. Barzegar |
| author_sort | H. Barzegar |
| collection | DOAJ |
| description | Two important algebraic structures are S-acts and Boolean algebras. Combining these two structures, one gets S-Boolean algebras, equipped with a compatible right action of a monoid S which is a special case of Boolean algebras with operators. In this article, we considered some category-theoretic properties of the category Boo-S of all S-Boolean algebras with action-preserving maps between them which also preserve Boolean operations. The purpose of the present article is to study certain categorical and algebraical concepts of the category Boo-S, such as congruences, indecomposable objects, coproducts, pushouts, and free objects. |
| format | Article |
| id | doaj-art-b11d4d2eadbb46b496f7eeb341ca97ca |
| institution | DOAJ |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b11d4d2eadbb46b496f7eeb341ca97ca2025-08-20T03:20:51ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/3761080Boolean Algebras with Semigroup Operators: Free Product and Free ObjectsH. Barzegar0Department of MathematicsTwo important algebraic structures are S-acts and Boolean algebras. Combining these two structures, one gets S-Boolean algebras, equipped with a compatible right action of a monoid S which is a special case of Boolean algebras with operators. In this article, we considered some category-theoretic properties of the category Boo-S of all S-Boolean algebras with action-preserving maps between them which also preserve Boolean operations. The purpose of the present article is to study certain categorical and algebraical concepts of the category Boo-S, such as congruences, indecomposable objects, coproducts, pushouts, and free objects.http://dx.doi.org/10.1155/2023/3761080 |
| spellingShingle | H. Barzegar Boolean Algebras with Semigroup Operators: Free Product and Free Objects Journal of Mathematics |
| title | Boolean Algebras with Semigroup Operators: Free Product and Free Objects |
| title_full | Boolean Algebras with Semigroup Operators: Free Product and Free Objects |
| title_fullStr | Boolean Algebras with Semigroup Operators: Free Product and Free Objects |
| title_full_unstemmed | Boolean Algebras with Semigroup Operators: Free Product and Free Objects |
| title_short | Boolean Algebras with Semigroup Operators: Free Product and Free Objects |
| title_sort | boolean algebras with semigroup operators free product and free objects |
| url | http://dx.doi.org/10.1155/2023/3761080 |
| work_keys_str_mv | AT hbarzegar booleanalgebraswithsemigroupoperatorsfreeproductandfreeobjects |