Definition:Characteristic of Ring/Definition 1
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Let $n \cdot x$ be defined as in Definition:Power of Element.
The characteristic $\Char R$ of $R$ is the smallest $n \in \Z, n > 0$ such that $n \cdot 1_R = 0_R$.
If there is no such $n$, then $\Char R = 0$.
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): $\S 1.2$
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $4$: Fields: $\S 17$. The Characteristic of a Field
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 6$: Rings and fields
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 2.4$: The rational numbers and some finite fields