Definition:Ideal of Ring/Right Ideal
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This page is about Right Ideal of Ring in the context of Ring Theory. For other uses, see Ideal.
Definition
Let $\struct {R, +, \circ}$ be a ring.
Let $\struct {J, +}$ be a subgroup of $\struct {R, +}$.
$J$ is a right ideal of $R$ if and only if:
- $\forall j \in J: \forall r \in R: j \circ r \in J$
that is, if and only if:
- $\forall r \in R: J \circ r \subseteq J$
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $22$. New Rings from Old: Exercise $22.22$
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 6$: Rings and fields
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): ideal
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): ideal
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ideal
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): ideal