We give a construction of Wallman-type realcompactifications of a frame $L$ by considering regular sub $\sigma$-frames the join of which generates $L$. In particular, we show that the largest such regular sub $\sigma$-frame gives rise to the universal realcompactification of $L$.
@article{118761, author = {Nizar Marcus}, title = {Realcompactification of frames}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {36}, year = {1995}, pages = {347-356}, zbl = {0840.54027}, mrnumber = {1357534}, language = {en}, url = {http://dml.mathdoc.fr/item/118761} }
Marcus, Nizar. Realcompactification of frames. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 347-356. http://gdmltest.u-ga.fr/item/118761/
Stone-Čech compactification and dimension theory for regular $\sigma$-frames, J. London Math. Soc. 39 (1989), 1-8. (1989) | MR 0989914 | Zbl 0675.06005
Realcompactifications through zero-set spaces, Quaestiones Math. 6 (1983), 73-95. (1983) | MR 0700241 | Zbl 0521.54012
Realcompact spaces and regular $\sigma$-frames, Math. Proc. Camb. Phil. Soc. 96 (1984), 73-79. (1984) | MR 0743702 | Zbl 0547.54021
Stone Spaces, Cambridge Studies in Advanced Math. 3, Cambridge Univ. Press, 1982. | MR 0698074 | Zbl 0586.54001
Lindelöf locales and realcompactness, Math. Proc. Camb. Phil. Soc. 99 (1986), 473-480. (1986) | MR 0830360 | Zbl 0603.54021
${\Bbb N}$-Compact frames and applications, Doctoral thesis, McMaster University, 1990. | MR 1118300