Geodesic
Rigid extensions of $\ell$-groups of continuous functions
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 993-1014 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $C(X,\mathbb Z )$, $C(X,\mathbb Q )$ and $C(X)$ denote the $\ell $-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space $X$, respectively. Characterizations are given for the extensions $C(X,\mathbb Z )\leq C(X,\mathbb Q )\leq C(X)$ to be rigid, major, and dense.
Let $C(X,\mathbb Z )$, $C(X,\mathbb Q )$ and $C(X)$ denote the $\ell $-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space $X$, respectively. Characterizations are given for the extensions $C(X,\mathbb Z )\leq C(X,\mathbb Q )\leq C(X)$ to be rigid, major, and dense.
Classification : 06F20, 54C40, 54F65
Keywords: rigid extension; major extension; archimedean extension; dense extension 
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     author = {Knox, Michelle L. and McGovern, Warren Wm.},
     title = {Rigid extensions of $\ell$-groups of continuous functions},
     journal = {Czechoslovak Mathematical Journal},
     pages = {993--1014},
     year = {2008},
     volume = {58},
     number = {4},
     mrnumber = {2471161},
     zbl = {1174.06341},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a8/}
}
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Knox, Michelle L.; McGovern, Warren Wm. Rigid extensions of $\ell$-groups of continuous functions. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 993-1014. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a8/