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arXiv · 2407.07793

Artinian Meadows

João Dias·Bruno Dinis
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Abstract

We introduce the notion of Artinian meadow as an algebraic structure constructed from an Artinian ring which is also a common meadow, i.e.\ a commutative and associative structure with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero in a common meadow is an error term $\mathbb{a}$ which is absorbent for addition. We show that, in analogy with what happens with commutative unital Artinian rings, Artinian meadows decompose as a product of local meadows in an essentially unique way. We also provide a canonical way to construct meadows from unital commutative rings.

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João Dias, Bruno Dinis. 2024-07-10. Artinian Meadows. https://arxiv.org/abs/2407.07793

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