Can I get any reference(book or journal paper) for the theorem, Let R be a commutative ring, R is semisimple if and only if it is isomorphic to a direct product of a finite number of fields.
2026-04-08 07:37:48.1775633868
reference for theorem commutative ring R is semi simple iff direct product of fields
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This follows immediately from Artin-Wedderburn theorem. It states that a ring is semisimple iff it is a direct product of matrix rings over division rings (aka skew-fields); for them to be commutative, matrices have to be $1\times 1$, that is, isomorphic to scalars, and division rings have to be commutative, that is, fields.
Googling "Artin-Wedderburn theorem proof" yields a lot of results, like this, this, or this one.