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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.10885 |
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| _version_ | 1866929315906584576 |
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| author | Halušková, Emília Jakubíková-Studenovská, Danica |
| author_facet | Halušková, Emília Jakubíková-Studenovská, Danica |
| contents | A retract variety is defined as a class of algebras closed under isomorphisms, retracts and products. Let a principal retract variety be generated by one algebra and a set-principal retract variety be generated by some set of algebras. It is shown that (a) not each set-principal retract variety is principal, and (b) not each retract variety is set-principal. A class of connected monounary algebras $\mathcal{S}$ such that every retract variety of monounary algebras is generated by algebras that have all connected components from $\mathcal{S}$ and at most two connected components are isomorphic is defined, this generating class is constructively described. All set-principal retract varieties of monounary algebras are characterized via degree function of monounary algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10885 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On retract varieties of algebras Halušková, Emília Jakubíková-Studenovská, Danica Rings and Algebras 08A60, 08C99, 08A35 A retract variety is defined as a class of algebras closed under isomorphisms, retracts and products. Let a principal retract variety be generated by one algebra and a set-principal retract variety be generated by some set of algebras. It is shown that (a) not each set-principal retract variety is principal, and (b) not each retract variety is set-principal. A class of connected monounary algebras $\mathcal{S}$ such that every retract variety of monounary algebras is generated by algebras that have all connected components from $\mathcal{S}$ and at most two connected components are isomorphic is defined, this generating class is constructively described. All set-principal retract varieties of monounary algebras are characterized via degree function of monounary algebras. |
| title | On retract varieties of algebras |
| topic | Rings and Algebras 08A60, 08C99, 08A35 |
| url | https://arxiv.org/abs/2404.10885 |