Free word problems for additive relation algebras of modules

AbstractFor M an R-module, the set Su(M × M) of submodules of M × M is an additive relation algebra under lattice meet and join, composition of relations, unary converse (〈a, b〉 in ƒ# iff 〈b, a〉 ∈ ƒ), relational sum (〈a, b+c〉 ∈ ƒ + g if 〈a, b〉 ∈ ƒ and 〈 a, c〉 ∈ g), and several constants. For a ring R with unit, VR denotes the variety of additive relation algebras generated by {Su(M × M): M an R-module}.The analysis of these varieties includes an algorithm for recursively solving free word problems for VR in many cases, the classification of all the distinct varieties VR, a self-duality result for all VR, and a proof that VR is not finitely axiomatizable for R a field with characteristic zero, among other cases