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arXiv · 0903.5116

Remarks on the sequential effect algebras

Shen Jun·Wu Junde
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Abstract

In this paper, first, we answer affirmatively an open problem which was presented in 2005 by professor Gudder on the sub-sequential effect algebras. That is, we prove that if $(E,0,1, \oplus, \circ)$ is a sequential effect algebra and $A$ is a commutative subset of $E$, then the sub-sequential effect algebra $\bar{A}$ generated by $A$ is also commutative. Next, we also study the following uniqueness problem: If $na=nb=c$ for some positive integer $n\geq 2$, then under what conditions $a=b$ hold? We prove that if $c$ is a sharp element of $E$ and $a|b$, then $a=b$. We give also two examples to show that neither of the above two conditions can be discarded.

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Shen Jun, Wu Junde. 2009-03-30. Remarks on the sequential effect algebras. https://doi.org/10.1016/s0034-4877(09)90015-5

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