The \(n\)th root of sequential effect algebras. (English) Zbl 1311.81012
Summary: In 2005, S, Gudder [Int. J. Theor. Phys. 44, No. 12, 2199–2206 (2005; Zbl 1110.81014)] presented 25 problems of sequential effect algebras, the 20th problem asked: In a sequential effect algebra, if the square root of some element exists, is it unique? In this paper, we show that for each given positive integer \(n > 1\), there is a sequential effect algebra such that the \(n\)th root of its some element c is not unique, and the \(n\)th root of c is not the \(k\)th root of \(c(k < n)\). Thus, we answer the problem negatively.{
©2010 American Institute of Physics}
©2010 American Institute of Physics}
MSC:
| 81P10 | Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) |
| 03G12 | Quantum logic |
| 06C15 | Complemented lattices, orthocomplemented lattices and posets |
Citations:
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