e-book Computational Commutative Algebra 2: v. 2

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Computational Commutative Algebra 2

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Post as a guest Name. Email Required, but never shown. Featured on Meta. Table of Contents Frontmatter Chapter 1. Endomorphisms Abstract.

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Various characterizations of this ubiquitous condition are derived. The chapter ends by considering diagonalizable and trigonalizable endomorphisms. In the second chapter the theory of eigenfactors and eigenspaces is extended to commuting families of endomorphisms.

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Moreover, we study splitting endomorphisms, i. Finally, simultaneous diagonalization and trigonalization of commuting families are covered.

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More generally, commendable families are defined by the condition that their joint eigenspaces have the minimal possible dimension. One of the highlights of the chapter is the duality theorem which says that a family is commendable if and only if the dual vector space is a cyclic module over the dual family. In the fourth chapter we start to apply the linear algebra techniques developed in the earlier chapters to computational commutative algebra.

In addition to the generic approach, i. The chapter finishes with some recent insights into the calculation of the separable subalgebra.

However, over the rational numbers, the technique of cloning leads to the hard problem of splitting polynomials over number fields, and it is here that the applications, as well as the book, come to their natural conclusion.