Definition:Proper Subring
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Definition
Let $\struct {R, +, \circ}$ be a ring.
A subring $S$ of $R$ is a proper subring of $R$ if and only if $S$ is neither the null ring nor $R$ itself.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): proper: 2.
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $5$: Rings: $\S 19$. Subrings: Example $30$