Abstract
Abstract The main classes of finite rings (f.r.) and modules interesting for applications are considered: Wedderburn rings, local, chain and Galois rings, (quasi)-Frobenius bimodules. Polynomials, functions, identities, matrices and linear substitutions over commutative chain f.r. (GE-rings) are described. As applications the results about standard bases of polynomial ideals, systems of polynomial equations, periodic properties of polynomial ideals are presented. Properties of matrices, linear sequences and (poly-)linear recurrences over GE-rings and Galois rings are shown. We state also the main results of the general theory of linear codes over finite modules and their representations.
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