We report a series of neural network models of semantic processing of single English words in the left and the right hemispheres of the brain. We implement the foveal splitting of the visual field and assess the influence of this splitting on a mapping from orthography to semantic representations in single word reading. The models were trained on English four-letter words, presented according to their frequency in all positions encountered during normal reading. The architecture of the model interacted with the training set to produce processing asymmetries comparable to those found in behavioral studies. First, the cueing effects of dominant and subordinate meanings of ambiguous words were different for words presented to the left or to the right of the input layer. Second, priming effects of groups of related words were stronger in the left input than the right input of the model. These effects were caused by coarser-coding in the right half compared with the left half of the model, an emergent effect of the split model interacting with informational asymmetries in the left and right parts of words in the lexicon of English. Some or all of the behavioral data for reading single words in English may have a similar origin.