The completeness problem in partial hyperclones. (English) Zbl 1105.08003
From the author’s abstract: “The composition-closed sets of partial multi-valued operations, called partial hyperclones, defined on the finite set \(\{0,1,\dots,k-1\}\) \((k\geq 2)\) are investigated. It is shown that the lattice of all partial hyperclones is dually atomic, i.e. any non-full partial hyperclone is contained in a maximal partial hyperclone. Based on this, some completeness criteria in the full partial hyperclone are established. Next, the total list of maximal restriction-closed partial hyperclones is obtained and, thus, the completeness problem with respect to compositions and restrictions of partial hyperclones is solved.”
Reviewer’s note: The author poses the question: Does there exist a binary Sheffer partial hyperoperation and also a binary Sheffer hyperoperation for any \(k\) \((k \geq 2)\)?
Reviewer’s note: The author poses the question: Does there exist a binary Sheffer partial hyperoperation and also a binary Sheffer hyperoperation for any \(k\) \((k \geq 2)\)?
Reviewer: V. S. Ramamurthi (Jacksonville)
MSC:
| 08A40 | Operations and polynomials in algebraic structures, primal algebras |
| 08A02 | Relational systems, laws of composition |
| 08A55 | Partial algebras |
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