We understand matrices up to similarity because the space of matrices forms an algebra, and properties of that algebra, like Jordan decomposition, come to bear. Spaces of tensors usually do not form an algebra, however there are situations where they can be embedded non-trivially into an algebra, and in turn properties of that algebra can inform our study of those tensors. In particular, when we can implement this algebra within software, we can construct things like adjoint operators. These adjoint operators can, in turn, be used to construct invariants of tensors. This project builds on recent work on ExteriorExtensions [5] by increasing the functionality to include adjoining a larger variety of modules to spaces of tensors and constructing algebras out of these. A pay-off of this work would possibly be a way to find maximizers of these invariants, like was done in [2]. The application to quantum information theory of this work is that if we can find tensors that maximize (the absolute value of) an invariant, this should inform the development of quantum information since distance to invariant hyper surfaces can be one way to measure entanglement. Tensors represent quantum states, and states with higher entanglement can carry more information. This project will be led by Luke Oeding.