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It does not work like that. I'm pretty hopeless at explaining in any understandable manner but I'll try.
A gene can only be dominant, (recessive, incompletely dominant or co-dominant) to genes which are alleles. Alleles are alternative genes which could be in the gene pair. Sometimes there are only two alleles, sometimes there are quite a few. "Black" is the effect of various genes & is not an allele of dominant white. I think the known alleles of dominant white are: i+ (not dominant white), I^D (dun), I^S (smokey). i+, the wild type "not dominant white" gene, allows black but it is not, itself, black.
You forgot I (dominant white) itself
Unrelated genes are neither dominant nor recessive towards each other, only towards other variations of the gene at their specific loci.
Think of a gene as having a particularly shaped hole in a child's shape sorter. Only blocks that are shaped to fit the hole can fill that spot, although they could be red/blue/pink/green/purple polka-dotted. These blocks are the alleles for that gene.
In most cases there are two identically shaped holes, and each will hold one block of the correct shape. Dominance refers to the way these two identically shaped blocks, which may or may not have different colours/patterns translates into the appearance (phenotype).
If one of the blocks is dominant to the other, it will override the more recessive block. If incompletely dominant, the appearance will fall in between the dominant and recessive blocks, and if recessive, it may show in down or first feathering, but will not show in normal adult plumage (when a more dominant allele is present). There is also a variation called co-dominance, wherein both blocks are fully expressed, but I am not aware of any genes relating to chickens that have co-dominant alleles.