Central simple algebras are a fundamental concept in algebra, particularly in the study of algebraic structures over fields. Let's break down what central simple algebras are: 1. **Algebra**: In the context of central simple algebras, an algebra refers to a vector space equipped with a multiplication operation that is associative and distributes over vector addition.
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A central simple algebra over a field is a finite-dimensional associative -algebra that is a simple ring and whose center is exactly .