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- $0_R + 0_R = 0_R$
- $0_R \circ 0_R = 0_R$
Also known as
Some authors refer to this as the zero ring, others as the degenerate ring.
Still others refer to it as the trivial ring, but this term has been defined differently elsewhere.
- Null Ring is Trivial Ring in which it is seen that the null ring is a trivial ring and therefore a commutative ring.
- Uniqueness of Null Ring
- Results about the null ring can be found here.
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): $\S 21$: Example $21.4$
- 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): $\S 3.1$: Direct sums
- 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): $\S 1$