Abstract

The work builds on the algebraic theory of polynomials Tue. The theory is based on the study of submodules of Z[????]-module Z[????] 2 . Considers submodules that are defined by one defining relation and one defining relation ????-th order. More complex submodule is the submodule given by one polynomial relation. Sub par Tue ????-th order are directly connected with polynomials Tue ????-th order. Using the algebraic theory of pairs of submodules of Tue ????-th order managed to obtain a new proof of the theorem of M. N. Dobrowolski (senior) that for each ???? there are two fundamental polynomial Tue ????-th order, which are expressed through others. Basic polynomials are determined with an accuracy of unimodular polynomial matrices over the ring of integer polynomials. In the work introduced linear-fractional conversion of TDP-forms. It is shown that the transition from TDP-forms associated with an algebraic number ???? to TDP-the form associated with the residual fraction to algebraic number ????, TDP-form is converted under the law, similar to the transformation of minimal polynomials and the numerators and denominators of the respective pairs of Tue is converted using the linear-fractional transformations of the second kind.

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