Abstract
If K is any field, an infinite product K I is a nonsemisimple ring. But it is the product of the (nonisomorphic) simple right ideals \({\left\{ {{P_i}} \right\}_{i \in I}}\) where P i and q i : K → K I are the canonical injections. Indeed, it suffices to remark that isomorphic rings (or even modules) have the same annihilator ideal.
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© 1998 Springer Science+Business Media Dordrecht
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Cǎlugǎreanu, G., Hamburg, P. (1998). Semisimple Rings. In: Exercises in Basic Ring Theory. Kluwer Texts in the Mathematical Sciences, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9004-4_29
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DOI: https://doi.org/10.1007/978-94-015-9004-4_29
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4985-8
Online ISBN: 978-94-015-9004-4
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