Morita equivalence lemma for arbitrary algebras

Morita equivalence lemma for arbitrary algebras

Let us consider first an example of Morita equivalence; thus, for an integer $ n \geq 1$ , let $ Mat_n(A)$ be the algebra of $ n \times n$ -matrices with entries in an algebra $ A$ . The following is a typical example of Morita equivalence that involves noncommutative algebras.

Theorem 1.1   Morita equivalence Lemma for arbitrary algebras

For any algebra $ A$ and any integer $ n \geq 1$ , the algebras $ A$ and $ Mat_n(A)$ are Morita equivalent.

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