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A characterization of the n-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem
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A characterization of the n-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem
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| dc.contributor.author | Climent Vidal, J. | |
| dc.contributor.author | Cosme i Llópez, Enric | |
| dc.date.accessioned | 2019-02-27T14:41:25Z | |
| dc.date.available | 2019-11-15T05:45:05Z | |
| dc.date.issued | 2018 | |
| dc.identifier.citation | Climent Vidal, J. Cosme i Llópez, Enric 2018 A characterization of the n-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem Quaestiones Mathematicae 1 18 | |
| dc.identifier.uri | http://hdl.handle.net/10550/69207 | |
| dc.description.abstract | A theorem of single-sorted algebra states that, for a closure space (A, J ) and a natural number n, the closure operator J on the set A is n-ary if and only if there exists a single-sorted signature Σ and a Σ-algebra A such that every operation of A is of an arity ≤ n and J = SgA, where SgA is the subalgebra generating operator on A determined by A. On the other hand, a theorem of Tarski asserts that if J is an n-ary closure operator on a set A with n ≥ 2, then, for every i, j ∈ IrB(A, J ), where IrB(A, J ) is the set of all natural numbers which have the property of being the cardinality of an irredundant basis (≡ minimal generating set) of A with respect to J , if i < j and {i + 1, . . . , j − 1} ∩ IrB(A, J ) = Ø, then j − i ≤ n − 1. In this article we state and prove the many-sorted counterparts of the above theorems. But, we remark, regarding the first one under an additional condition: the uniformity of the many-sorted closure operator. | |
| dc.language.iso | eng | |
| dc.relation.ispartof | Quaestiones Mathematicae, 2018, p. 1-18 | |
| dc.subject | Matemàtica | |
| dc.title | A characterization of the n-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem | |
| dc.type | journal article | es_ES |
| dc.date.updated | 2019-02-27T14:41:25Z | |
| dc.identifier.doi | 10.2989/16073606.2018.1532931 | |
| dc.identifier.idgrec | 130222 | |
| dc.accrualmethod | ||
| dc.embargo.terms | 1 year | |
| dc.rights.accessRights | open access | es_ES |
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