Entangled and skew polynomials

The study of rings of entangled polynomials is extended to the case where the m-nomials have coefficients in a ring rather than only a field. Ring-theoretic properties of these rings, such as their Jacobson radicals, chain conditions, units, and the existence of roots, are among the topics considered. The study relies on the establishment of connections with skew polynomial rings. In particular, it is shown that every ring of m-nomials is isomorphic to a skew polynomial ring induced by a cyclic permutation. As an application, this result yields that every skew polynomial ring with an abstract automorphism of finite order can be viewed as a subring of a skew polynomial ring with a specific cyclic permutation.