Constructing Witt–Burnside rings

Constructing Homomorphism Spaces and Endomorphism Rings

Abstract We present a new deterministic algorithm for constructing homomorphism spaces and endomorphism rings of finite dimensional modules. The modules are given via vertex projective presentations over path algebras and finite dimensional quotients of path algebras. We use the theory of right Gröbner bases to encode modules and to construct appropriate systems of equations for computing homom...

Constructing Division Rings as Module-theoretic Direct Limits

If R is an associative ring, one of several known equivalent types of data determining the structure of an arbitrary division ring D generated by a homomorphic image of R is a rule putting on all free R-modules of finite rank matroid structures (closure operators satisfying the exchange axiom) subject to certain functoriality conditions. This note gives a new description of how D may be constru...

Compact Logics in Zfc: Constructing Complete Embeddings of Atomless Boolean Rings

Suppose for simplicity that T is first order with Skolem functions in strong enough sense. We prove, in ZFC, that is has a model B in which for any two atomless Boolean algebras definable in it, any isomorphism or even complete embedding from one to the other is definable in the model. This has consequences on the compactness of logics gotten by extending first order logic by quantifying over s...

An algorithm for constructing a basis for Cr-spline modules over polynomial rings

Let 2 be a polyhedral complex embedded in the euclidean space Ed and Sr(2), r ≥ 0, denote the set of all Cr-splines on 2. Then Sr(2) is an R-module where R = E[x1, . . . , xd] is the ring of polynomials in several variables. In this paper we state and prove the existence of an algorithm to write down a free basis for the above R-module in terms of obvious linear forms defining common faces of m...

Differential Polynomial Rings of Triangular Matrix Rings