On the Directly and Subdirectly Irreducible Many-Sorted Algebras
Abstract: A theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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On the Directly and Subdirectly Irreducible Many-Sorted Algebras ; volume:48 ; number:1 ; year:2015 ; pages:1-12 ; extent:12
Demonstratio mathematica ; 48, Heft 1 (2015), 1-12 (gesamt 12)
- Creator
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Climent Vidal, J.
Soliveres Tur, J.
- DOI
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10.1515/dema-2015-0001
- URN
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urn:nbn:de:101:1-2411181439591.679722131965
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:27 AM CEST
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Associated
- Climent Vidal, J.
- Soliveres Tur, J.
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