Simple ring - Wikipedia
WEBIn abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular, a commutative ring is a simple ring if and only if it is a field. The center of a simple ring is necessarily a field.
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Simple Ring -- from Wolfram MathWorld
WEBAug 22, 2024 · Simple Ring. A nonzero ring whose only (two-sided) ideals are itself and zero. Every commutative simple ring is a field. Every simple ring is a prime ring.
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Simple ring - Encyclopedia of Mathematics
WEBNov 26, 2016 · Simple ring. A ring, containing more than one element, without two-sided ideals (cf. Ideal) different from 0 and the entire ring. An associative simple ring with an identity element and containing a minimal one-sided ideal is isomorphic to a matrix ring over a some skew-field (cf. also Associative rings and algebras).
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