Superposition theorem proving for abelian groups represented as integer modules

Superposition Theorem Proving for Albelian Groups Represented as Integer Modules

We deene a superposition calculus specialized for abelian groups represented as integer modules, and show its refutational completeness. This allows to substantially reduce the number of inferences compared to a standard superposition prover which applies the axioms directly. Speciically, equational literals are simpliied, so that only the maximal term of the sums is on the left-hand side. Only...

Superposition with completely built-in Abelian groups

A new technique is presented for superposition with first-order clauses with built-in Abelian groups (AG). Compared with previous approaches, it is simpler, and AG-unification is used instead of the computationally more expensive unification modulo associativity and commutativity. Furthermore, no inferences with the AG axioms or abstraction rules are needed; in this sense this is the first appr...

Modules for Elementary Abelian p-groups

Let E ∼= (Z/p)r (r ≥ 2) be an elementary abelian p-group and let k be an algebraically closed field of characteristic p. A finite dimensional kE-module M is said to have constant Jordan type if the restriction of M to every cyclic shifted subgroup of kE has the same Jordan canonical form. I shall begin by discussing theorems and conjectures which restrict the possible Jordan canonical form. The...

non-divisibility for abelian groups

Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting   all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...

A Superposition Calculus for Divisible Torsion-Free Abelian Groups