Definition:Ideal of Ring/Left Ideal
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Definition
Let $\left({R, +, \circ}\right)$ be a ring.
Let $\left({J, +}\right)$ be a subgroup of $\left({R, +}\right)$.
$J$ is a left ideal of $R$ if and only if:
- $\forall j \in J: \forall r \in R: r \circ j \in J$
Also see
Sources
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Algebraic Concepts
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Exercise $22.22$
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 6$: Rings and fields