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2017 | OriginalPaper | Chapter

1. First Principles

Author : Gene Freudenburg

Published in: Algebraic Theory of Locally Nilpotent Derivations

Publisher: Springer Berlin Heidelberg

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Abstract

Throughout this chapter, assume thatB is an integral domain containing a fieldk of characteristic zero.B is referred to as ak-domain.B ^∗ denotes the group of units ofB and frac(B) denotes the field of fractions ofB. Further, Aut(B) denotes the group of ring automorphisms ofB, and Aut_k(B) denotes the group of automorphisms ofB as ak-algebra. IfA ⊂B is a subring, then tr.deg_A B denotes the transcendence degree of frac(B) over frac(A). The ideal generated byx ₁, …, x _n ∈B is denoted by either (x ₁, …, x _n) orx ₁ B + ⋯ +x _n B. The ring ofm ×n matrices with entries inB is indicated by \(\mathcal{M}_{m\times n}(B)\) and the ring ofn ×n matrices with entries inB is indicated by \(\mathcal{M}_{n}(B)\). The transpose of a matrixM isM ^T.

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next chapter Further Properties of LNDs

The termplinth commonly refers to the base of a column or statue.

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Title: First Principles
Author: Gene Freudenburg
Publisher: Springer Berlin Heidelberg
Book: Algebraic Theory of Locally Nilpotent Derivations
Print ISBN: 978-3-662-55348-0

Electronic ISBN: 978-3-662-55350-3

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-662-55350-3_1

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