Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on the sequential effect algebras   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.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci