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Semisimple Ring

A semisimple ring is a semiprime ring which is also an Artinian ring.

Every semisimple ring is a pure semisimple ring on both sides. Pure semisimplicity requires direct sums of finitely generated modules, rather than simple modules. The pure semisimplicity conjecture concerns whether the right-sided property forces the left-sided property and finite representation type.

See also

Artinian Ring

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References

Herstein, I. N. "Semisimple Rings." §1.2 in Noncommutative Rings. Washington, DC: Math. Assoc. Amer., pp. 52-56, 1968.Šaroch, J. "Pure Semisimplicity Conjecture and Artin Problem for Dimension Sequences." J. Pure Appl. Algebra 225, 106745, 2021. https://doi.org/10.1016/j.jpaa.2021.106745.

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Semisimple Ring

Cite this as:

Weisstein, Eric W. "Semisimple Ring." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SemisimpleRing.html

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