In this note we show that a Noetherian module has a dual module if and only if it satisfies AB5*. A connection between completeness and AB5* is also established. In this note we relate completeness, quasi-completeness, the A B5* condition, and duality. The main result is that a Noetherian R-module has a dual module if and only if it satisfies A B5*. Throughout this note R will denote a commutat...

Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t]-submodules Im(1− t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Zn[t ]/(t− a) where gcd(n, a) = 1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. We...

Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t]-submodules Im(1 − t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Zn[t ]/(t − a) where gcd(n, a) = 1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. ...