Homotopy Type Theory algebra (ring theory) > history (Rev #2, changes)

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Definition

Given a commutative ring $R$, an $R$-algebra is a ring $\mathrm{<span><del\; class="diffmod">\; A</del><ins\; class="diffmod">\; R</ins></span>}$ A R , with an$R$-algebra is a ring $A$ with a ring homomorphism? $f:R \to A$.

Properties

An If algebra in ring theory is an$R$ is a commutative ring and the $R$-algebra $A$ has a commutative ring homomorphism? $g:R \to Z(A)$ into the center $Z(A) \subseteq A$ of $A$, as well as a term $a: i \circ g = f$, where $i:Z(A) \subseteq A$ is the associated monic function for subtype $Z(A)$ of $A$, then $A$ is an associative? unital? algebra in module theory.

See also

• ring
• commutative ring
• commutative algebra (ring theory)
• algebra (module theory)