$𝑅$ -monoid

Let $𝑅$ be a commutative ring. An $𝑅$ -monoid $𝑇$ is a monoid in the category [[Category of modules over a commutative ring| $𝑅 𝖬 𝗈 𝖽$ ]]. More concretely, an $𝑅$ -monoid $𝑇$ can be viewed in two equivalent ways: calg

As an R-algebra $𝑇$ which is unital and associative;
As a ring $𝑇$ equipped with a homomorphism $𝑅 \to Z (𝑇)$ into its centre.

This is of course a strenthening of R-semigroup. It follows every ring is a Integers-monoid in a unique way.

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$𝑅$ -monoid

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Table of Contents

𝑅-monoid

See also

Graph View

Backlinks

$𝑅$ -monoid