Published on: 2025-06-11 14:59:52
The Two Ideals of Fields By Susam Pal on 27 May 2025 A field has exactly two ideals: the zero ideal, which contains only the additive identity, and the whole field itself. These are known as trivial ideals. Further if a commutative ring, with distinct additive and multiplicative identities, has no ideals other than the trivial ones, then it must be a field. These two facts are elegant in their symmetry and simplicity. In this article, we will explore why these facts are true. Familiarity with
Keywords: cdot ideal ideals multiplication ring
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