C-connected frame congruences

Document Type : Research Paper


1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.

2 Department of Applied Mathematics and CE-ITI, MFF, Charles University, Malostransk\'e n\'am. 24, 11800 Praha 1, Czech Republic.


We discuss the congruences $\theta$ that are connected as  elements of the (totally disconnected) congruence frame $\CF L$,  and show that they are in a one-to-one correspondence with the completely prime elements of $L$, giving an explicit formula. Then we investigate those frames $L$ with enough connected congruences to cover the whole of $\CF L$. They are, among others, shown to be $T_D$-spatial;  characteristics for some special cases (Boolean, linear, scattered and Noetherian) are presented.


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