Monadic MV-algebras I: a study of subvarieties
In this paper, we study and classify some important subvarieties of the variety of monadic MV-algebras. We introduce the notion of width of a monadic MV-algebra and we prove that the equational class of monadic MV-algebras of finite width k is generated by the monadic MV-algebra [0, 1] k. We describ...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2014 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/29824 |
| Online Access: | http://hdl.handle.net/11336/29824 |
| Access Level: | Open access |
| Keyword: | Monadic Mv-Algebras Functional Representation Subvarieties Equational Bases https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | In this paper, we study and classify some important subvarieties of the variety of monadic MV-algebras. We introduce the notion of width of a monadic MV-algebra and we prove that the equational class of monadic MV-algebras of finite width k is generated by the monadic MV-algebra [0, 1] k. We describe completely the lattice of subvarieties of the subvariety V([0, 1] k) generated by [0, 1] k. We prove that the subvariety generated by a subdirectly irreducible monadic MV-algebra of finite width depends on the order and rank of ∀A, the partition associated to A of the set of coatoms of the boolean subalgebra B(A) of its complemented elements, and the width of the algebra. We also give an equational basis for each proper subvariety in V([0, 1] k). Finally, we give some results about subvarieties of infinite width. |
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