Elements with Support in Ideal form Submagma of Direct Product
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Theorem
Let $\family {S_i, \circ_i}_{i \mathop \in I}$ be a family of magmas with identity.
Let $\ds S = \prod_{i \mathop \in I} S_i$ be their direct product.
Let $J \subset I$ be an ideal of $I$.
This article, or a section of it, needs explaining. In particular: The link to ideal suggests that $I$ would need to be an ordered set, which does not appear to be the case here. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |
Let $T = \set {s \in S: \map \supp s \in J}$ where $\supp$ denotes support.
Then $T$ is a submagma of $S$.
Proof
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