Linear Algebra for Computational Sciences and Engineering by Ferrante Neri

Author:Ferrante Neri
Language: eng
Format: epub, pdf
ISBN: 9783030213213
Publisher: Springer International Publishing

Proof

Let us consider three elements a, b, c ∈ R with c ≠ 0R such that ac = bc. It follows that

Since is an integral domain (hence without zero divisors) and c ≠ 0R it follows that necessarily . This fact means that

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7.4.2 Fields

Definition 7.30

Let be a ring and a ∈ R. The element a is said to be invertible if there exists and element b ∈ R such that ab = 1R. The element b is said inverse of the element a.

Proposition 7.17

Let be a ring and a ∈ R. The inverse element of a, when it exists, is unique.

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