Mathematical Sciences: Universal Algebra and Lattice Theory

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This project is concerned with the study of basic problems in universal algebra and lattice theory. The specific areas of investigation will be the study of the complexity of certain algorithms in finitely presented lattices; modular congruence varieties; the determination of a common generalization to Ore's and Jonsson's theorems on direct decompositions; development of a computer algebra system dealing with finitely presented lattices; and projective planes over prime fields. Lattices are discrete mathematical objects with a structure reflecting to some extent the structure of set theory or logic. This very weak structure means that lattices can be found in many mathematical environments. It also means that problems are easy to state, difficult to solve and of a very general nature.