A new model for associative memories is proposed in this paper. The mathematical tools used in this new model, include two binary operators designed specifically for the memories developed here. These operators were arbitrarily named as the first two letters from the Greek alphabet: α and β . The new associative memories ( αβ ) are of two kinds and are able to operate in two different modes. The operator α is useful at the learning phase, and the operator β is the basis for the pattern recall phase. The properties within the algebraic operators α and β , allow the αβ memories to exhibit similar characteristics to the ones inherent to the binary version of the morphological associative memories, in the sense of: learning capacity, type and amount of noise against which the memory is robust, and the sufficient conditions for perfect recall. Moreover, it is important to point out that the arithmetic density of the proposed memories is smaller than the arithmetic density exhibited by the morphological ones. The main reason for taking the morphological associative memories as the reference point for the genesis of the proposed ones, consist in that the authors of the first ones have already shown that the morphological associative memories are superior in some aspects to the known models of associative memories, up to the beginning of the third millenium.